Excited states of ¹⁹⁹,²⁰¹,²⁰³Tl populated in the (α, 2nγ) and (d,3nγ) reactions


Full text


(cc,2ny) AND (d,3ny) REACTIONS



A thesis submitted for the degree of DOCTOR OF PHILOSOPHY

in the

Department of Nuclear Physics Research School of Physical Sciences

Australian National University



The work described in this thesis was done at the Department of Nuclear Physics under the joint supervision of Professor J.O. Newton and Dr G.D. Dracoulis. It was Professor Newton’s idea to study the odd-mass T1 isotopes and Dr Dracoulis suggested the spin alignment measurement described in Appendix 1.

The main burden of the experimental work was shared between my supervisors and myself. We were assisted by Drs J.R. Leigh and

S.M. Ferguson on a number of occasions. The data analysis was done by myself using my own computer programs and many of those already available within the department. Dr I.G. Graham developed the coincidence sorting program specifically for those of us who were accumulating multi­

dimensional data on magnetic t apes. The program for calculating the energy levels of a symmetric rotor-plus-particle system (chapter 4) and the program for calculating the attenuation coefficients (Appendix 1) were written by myself. I extensively modified a program written by Dr Ferguson for calculating the DCO ratios of chapter 5.

Much of the material in chapters 3 and 4 appears in a paper entitled "A Study of States in 20 1 , 20 3'pi Using The (d,3ny) Reaction: A New %

Band", by M.G. Slocombe, J.O. Newton and G.D. Dracoulis, which has been accepted for publication by the journal "Nuclear Physics".


1 am very grateful to have had the opportunity to study at the department as an ANU research scholar and would like to thank the many people who have made my stay here such a pleasurable one.

Canberra, 1976.

J A . (j





This thesis describes studies of the nuclei 1 99,20 1 > 203T 1 _

The nuclei 201 > 20 3 T1 were formed in (d,3n) reactions. Studies

of the de-excitation y-rays are detailed and level schemes are deduced

for both isotopes. Evidence is presented for the existence in 2 0 *T1

of a rotational band built on the


isomeric state at 920 keV. The

band is compared to the


bands occurring in the odd-mass isotopes

191 199^2 anci is shown to be well described by a symmetric rotor-plus-

particle model. The model predictions for the low-lying positive parity

states are also considered and satisfactory agreement with experimental

data is obtained. No


band was observed in 203T1 and possible

interpretations of this result are presented. The shapes of 201T1 and

203T1 are discussed.

The 1


l39y^ reaction has been studied in an attempt to

identify low spin levels predicted to arise from the lhg proton state


by the asymmetric rotor-plus-particle model. Seven new levels in 199T1

are proposed and their properties are compared with the model predictions.

Angular distributions of the y-transitions between members of the

ground state rotational band in each of the nuclei 158Dy, 16t+Er and

18 8yb have been measured following (d,3n) reactions. The statistical

alignment tensors and the attenuation coefficients of the alignment for

the 4+ , 6+ , 8+ and 10+ band members are deduced and compared with some




Preface ii

Abstract iv



2.1 Particle, xny Reactions 13

2.1.1 The Formation and Decay of the Compound

Nucleus 13

2.1.2 Gamma-Ray Spectroscopy 20

2.2 Beams, Targets and Detectors 23

2.3 The Experiments 26

2.3.1 The y-y Coincidence Experiment 27 2.3.2 Gamma-ray Angular Distributions 27 2.3.3 Gamma-ray Excitation Functions 29

2.3.4 The d-y Delay Experiment 30

2.3.5 The Low Energy y-ray Spectrum 30

2.3.6 The n-y Coincidence Experiment 31


AND 203T1 32

3.1 The Gamma-Rays and Their Properties 32

3.2 The Level Schemes 42

3.2.1 The Level Scheme for 201T1 42

3.2.2 The Level Scheme for 203T1 46

3.3 Level Spins 48

3.3.1 Spins for Levels of 201T1 51

The 1135, 1291 and 1414 keV levels 51 The 1239, 1572 and 1962 keV levels 52

The 2015 keV level 53

3.3.2 Spins for Levels of 2^3T1 53

The 1074, 1184 and 1218 keV levels 54

The 1450 and 2038 keV levels 35




THE SYMMETRIC ROTOR-PLUS-PARTICLE MODEL 57 4.1 The Symmetric Rotor-Plus-Particle Model 57

4.1.1 The Particle Energies 59

4.1.2 The Rotational Energies and The Rotation

Particle Coupling 64

4.1.3 The Recoil Term 68

4.1.4 The Modified Core and The Inertial Parameters 69 4.2 Model Calculations for 201T1 and 203T1 70

4.2.1 The Core 70

4.2.2 The Particle Energies and The Bandheads 72 4.2.3 Some Approximations for the Rotational

Energies 75

4.2.4 The Calculated Energy Levels 77

4.2.5 Transition Probabilities, Hole Strengths

and Magnetic Moments 82

4.2.6 Another Calculation for the Band 87

4.3 Shapes and Stability 89

4.3.1 The Shape of the Unobserved % State in

203T1 89

4.3.2 The Shape of the Ground State 90

4.3.3 Coexistence 91

4.4 Some Level Systematics 92

CHAPTER 5 — A SEARCH FOR ASYMMETRIC ROTOR STATES IN 199T1 94 5.1 The Asymmetric Rotor-Plus-Particle Model 95

5.2 Experimental Method 100

5.2.1 Choice of Technique 100

5.2.2 Experimental Details 101

The coincidence measurements 102

The remaining measurements 108

5.3 Results and Analysis 109

5.3.1 The 199T1 y-rays 109

5.3.2 Angular Correlations 112

5.4 The Level Scheme 115

5.5 Level Spins 118

5.5.1 The 1410, 1495 and 1684 keV Levels 118 5.5.2 The 1556, 1930, 2111 and 2134 keV Levels 120 5.5.3 Additional Information from the DCO Ratios 121

5.5.4 Some Evidence from 3-Decay 124



A P P E N D I X 1 — A SPIN A L I G N M E N T M E A S U R E M E N T 127

A1 .1 T he E x p e r i m e n t and The Res u l t s 127

A 1 .2 Di s c u s s i o n 133

A1 .3 The D e r i v a t i o n of The A t t e n u a t i o n for the

A l i g n m e n t in the C o m p o u n d N u c l e u s 137

A P P E N D I X 2 — R O T A T I O N A L M A T R I X E L E M E N T S 139

A 2 .1 The T e r m A R 2 139

A2.2 The T e r m B R 4 140

A 2 .3 The T e r m C R 6 141

A2.4 C o r i o l i s O p e r a t i o n s 141

A2.5 C l a s s i f i c a t i o n of T erms by Aft 143



The odd-mass T1 isotopes have been of considerable interest to nuclear physicists for a number of years and it is appropriate to begin a study such as this with some remarks on the progress already made towards an understanding of their behaviour. In this way the experiments and calculations to be presented in the subsequent chapters may be given their historical perspective. Furthermore, an opportunity arises to introduce the nuclear models with which we shall be concerned.

It was known as early as 1930 that the ground state spins of the two stable isotopes 20 3T1 and 205T1 were


(Fu69), a result explained in 1949 by Maria Mayer in terms of the newly proposed shell model with spin-orbit coupling (Ma49). In this model each nucleon was considered to move independently of other nucleons but in a potential well

representing their average attractive force. With a spherical harmonic oscillator potential well and a force causing particles with total angular momentum j =

Z + h

to be more strongly bound than those with j =

Z - h (Z

is the orbital angular momentum and


is the intrinsic spin) it was possible to account for the unusual stability of nuclei possessing "magic" numbers of protons or neutrons. The magic nature of the proton numbers 50, 82 and 126 is apparent in fig.1.1, where the shell model states (each of which can be occupied by a maximum of 2j+l particles) are labelled in the usual spectroscopic notation. The ground states of 203T1 and 205T1 could be identified with the 3s-, shell model state.


Z* 126




considerable influence on the interpretation of the experimental data accumulated on the T1 isotopes in the 1950s. In 1957 Bergström and Andersson (Be57), in their summary of the available results, classified

the ground and first excited states of the odd nuclei 195 207T1 as the s^ and d 3^ shell model states and the second excited state observed in

*T1 as the d 5y shell model state. An additional state, decaying 195- 205'

by an isomeric transition, had been assigned to both 195T1 and 197T1 by Andersson

et al

(An57) following the 3-decays of the corresponding Pb isotopes. They claimed that in the case of 197T1 this transition populated the second excited state and, since the K/L electron conversion ratio indicated an E3 multipolarity, they identified the isomeric state with the h ^ shell model state. The data on 195T1 could


be accounted for in the same way.

A Coulomb excitation study by McGowan and Stelson (Mc58) subsequently gave a degree of support to the shell model description of 203T1 and

205T1. Single particle transitions accompanied by Ml radiation are allowed only if they occur between states of the same orbital angular momentum. The shell model therefore predicts an allowed d ^ do. Ml



transition between the second and first excited states but forbids a -> s1 transition from the first excited state to ground. The experimental results showed that the 5/? -> V2 transitions in 203T1 and

205T1 were predominantly Ml, and had a strength comparable to the single particle estimate, while the -> V2 transitions were predominantly E2 and had only a small Ml strength. A calculation for 205T1 which included the residual interaction between the proton hole and the two neutron holes in the N=126 shell was able to account for the fact that the

3/2 -> V2 Ml component was not strictly forbidden (Si61) .


of effort when there were several particles or holes outside the closed shells. However, simplifications of the nuclear force, and models in which the motions of these extra-core nucleons were treated collectively, allowed many of the properties of nuclei not in the immediate vicinity of the closed shells to be explained. Silverberg, who published the shell model calculation for 205T1 mentioned above, included in the same paper a calculation treating 205T1 as a single s^ proton hole coupled to a vibrating 2 06Pb core. This calculation was simpler and more successful than the shell model calculation and Silverberg was able to conclude that "the vibrational description of the core and the coupling to the last particle is a good and simple way to approximate the

fundamentally very complicated nucleon-nucleon force".

The suggestion that states of even-even nuclei in the region of the closed shells, such as 206Pb, could be treated as the states of a

vibrator had been made several years previously. Indeed, the possibility of nuclear oscillations resulting from the collective behaviour of

nucleons had been mooted in the 1930s (Bo36, Bo37). A digression on the development of collective models is in order at this point as we shall be applying such a model to the odd-mass T1 isotopes in a later chapter.

It is instructive to compare the forces operating within a nucleus with those in an atom. The relatively large mass of the nucleus ensures that it dominates atomic behaviour. The electrons are strongly


collective states and data gathered in the early 1950s indicated that many of the low-lying states of even-even nuclei were of this type.

Near the closed shells, they could be interpreted as nuclear vibrations, while in the regions far from the closed shells they could be interpreted as nuclear rotations (see, for example, Mo 5 7 ) .

The most striking evidence for rotational behaviour was the often excellent agreement of the spectra of the even-even nuclei with the

1(1+1) dependence predicted by the rotational model, I being the total angular momentum, or spin, of the rotating nucleus. The spin sequence was 0 + , 2+ , 4+ , ... , as expected. It had already been shown by

Rainwater (Ra50) that particles outside the closed shells could be expected to deform the nuclear shape. When there were many such particles, the deformation was large, as evidenced by the electric quadrupole moments, and the energy required for collective rotations

was less than that required for vibrational or single particle excitations.

Evidence for vibrational behaviour in nuclei near the closed shells was provided by the fact that the second excited state was observed to have an excitation energy approximately twice that of the first excited state and to have a spin which was sometimes 0+ or 2+ , rather than 4+ . Additional evidence came from the identification of a low-lying 3 state

in some nuclei. The large values of the reduced transition probability B(E2) for several observed decays in both the deformed and closed shell regions indicated that many particles were involved and therefore

confirmed the collective nature of the states.

As we saw in the case of 205T1, it was possible to treat an odd- mass nucleus as a particle coupled to a collective even-even core. The


the case of a particle of angular momentum j and a phonon (the vibrational quantum) of angular momentum R, the solution to the Schrödinger equation for zero coupling strength is a degenerate set of states with spins allowed by the vector addition of R and j. A finite coupling strength removed this degeneracy. The coupling of a 3pj neutron hole to the 3 vibration of 208Pb to form ^/2+ and states in 207Pb, and the coupling of a lhc^, proton to the same vibration to form a - 1 septuplet in 209Bi, are evidenced by the inelastic proton scattering experiments of Hafele and Woods (Ha66) . However, there are not many examples of such a weak coupling to vibrations and in most cases a rather large value of the coupling strength is required ("intermediate" coupling). In

Silverberg’s calculation for 205T1 the strength of the coupling to the 2+ vibration of the 206Pb core was sufficiently large that the s^ proton hole contributed significantly to the wave function of the first excited 3/2+ state and the hole to the wave functions of the V2 + ground state


-4-and the second excited state.

In the well deformed regions far from the closed shells the odd particle is strongly coupled to the potential well of the core. The presence of a deformation in this well splits the spherical shell model state of spin j into (2j + l)/2 components, with spins 3/2 , ... , j, and the energy spectrum characteristically consists of well-defined

bands of rotational states built on these particle states. Perturbations to the bands can occur through the Coriolis coupling (also called

rotation-particle coupling) of the angular momentum of the odd particle to the angular momentum of the core. At smaller deformations the

Coriolis coupling can become rather important and, as we shall see later, it can result in significant modifications to the band structure.


and identified with the h ^ y proton hole state of the spherical shell

model (An57). Some years after this Diamond and Stephens were able to

populate isomers in these nuclei and also in 193T1 and 199T1 by means

of reactions induced by heavy ions (Di63). However, they were unable

to confirm that their spins were 1 % • The E3 nature of the isomeric

transition was not disputed but rather the fact that it populated the

% +

second excited state. The new data on the relative transition

intensities were inconsistent with a cascade through the 54 + state and

strongly suggested direct population of the 72 first excited state, indicating a spin of


for the isomer.

It can be seen from fig.1.1 that the lowest-lying 72 spherical

shell model state is the l h y state in the shell above the Z=82 closure.

This state would be expected at an excitation energy of several MeV,

yet the experimental excitation energy of the isomer was established as

less than 390 keV in 193T1, as 482 keV in 195T1, 607 keV in 197T1 and

749 keV in 199T1. The isomer detected in 201T1 by Gritsyna and Foster

(Gr65) was still at an excitation energy of only 915±10 keV (see fig.1.2).

The appearance of a low-lying % level therefore presented an interesting

problem, which Diamond and Stephens thought could be solved by considering

collective effects. One of their suggestions was that the character

of the isomer could be that of an h ^ proton hole coupled to a 2+ core



Further collective model calculations on the odd-mass T1 isotopes

were performed when the 204,206,2 O S p ^ ^ a ) 203,205,2 07^^ experiments of


et al

were reported (Hi66). The (t,a) results indicated a spreading

of the proton hole strength over many levels in 203T1 and 205T1,

encouraging Covello and Sartoris (Co67a) and Alaga and Ialongo (A167) to

extend the calculations of Silverberg to larger model spaces. For


proton holes to vibrations of up to three phonons in the even-even Pb core. They included a pairing interaction between the three holes and


all the hole states the 50 $ Z ^ 82 shell, but despite the good agreement with the data on the ground, first and second excited states, they were unable to account for a low-lying 9/£ isomer.

By 1970 it was apparent that the odd-mass T1 isotopes were rather more complicated than had hitherto been thought. Doebler (Do70) had used the high resolution which could by then be obtained with Ge (Li) detectors to investigate again the y-rays following the 3-decays of

199Pb and 2 0 ^ b . He was able to show that the level densities of 199T1 and 201T1 in the region between 1 MeV and 2 MeV were higher than

suggested by the model calculations. In addition, Newton

et at

(Ne70) had performed an in-beam study of the y-rays following the 197Au(a,2n)199T1 reaction, which revealed at least seven states in the same energy region with spins ^ 9/2, whereas the calculations had predicted that only one level, the h ^ proton level, would have such a spin.


The data therefore posed many new problems, but Newton and his collaborators were able to offer an important insight into the structure of the puzzling % isomer and the 1V2 > 1 % and states they

detected at higher excitation energies. They proposed that the


isomer was the 9/£ orbital arising from the splitting of the h y shell model state when this state is deformed. The 1^ , 1


and 154 states could then be interpreted as members of a rotational band built on the

isomer. Excellent evidence for the collective nature of the states was provided by the identification of very similar bands built on the

% isomers in the lighter odd-mass isotopes 192 197T1 and also of a


Since the T1 isotopes were generally thought to be spherical, the

possession of a stable deformation by the isomer required explanation.

Theoretical calculations (Ku68) indicated that the light doubly even

Hg nuclei, which can be considered as cores for the odd-mass T1 isotopes,

have a potential energy minimum at small oblate deformations. Now the

energy of an odd proton in the 94 orbital arising from the h g , shell

model state decreases rapidly with increasing oblate deformation and it

is possible to show that, at the deformation corresponding to the oblate

potential minimum of the core, the energy gained in this way is

sufficient to sustain a stable oblate deformation for the % state in

the odd-mass T1 isotope (Ne70) . The steady increase in the excitation

energy of the isomer with increasing mass number can be explained within

this model as a consequence of a corresponding decrease in the deformation

and depth of the core minimum.

It therefore seemed as though spherical and deformed states coexisted

in the light odd-mass T1 isotopes. The notion of shape coexistence was

by no means new as rotational bands had previously been proposed in the

closed shell nucleus 160 (Mo56, Bo64) and Mottelson and Nilsson (Mo59)

had suggested that states with quite different prolate deformations could

occur in the same nucleus in the region of neutron number N=90.

Experiments, such as those on 151Gd (K174) and 72Se (Ha74), and potential

energy calculations, such as those of Kolb and Wong (Ko75) for the even

Hg isotopes, now indicate that different shapes may coexist in a number

of nuclei. However, other interpretations of the data are sometimes

possible (see, for example, Dr76) and we shall be treating the evidence

for coexistence in the light odd-mass T1 isotopes more critically in a

later chapter.


et aZ

(St73) were able to confirm that the rotational model


the importance of this model in regions of moderate and small deformations.

They showed that the Coriolis coupling of the angular momentum of the odd

particle to the angular momentum of the rotating core could lead to

energy spectra quite different to those encountered in the well-deformed

region, enabling new data on band structure in the odd La isotopes (Le73)

and Hg isotopes (Pr74) to be explained. Another interesting result was

that at very small deformations the model predicted similar spectra to

those obtained in the weak coupling scheme which we mentioned earlier.

This implied that the distinction between the rotational and vibrational

regions was not as sharp as the information on the even-even nuclei had

once suggested. We shall be applying the same model to the states of

201T1 and 203T1 in chapter 4 where it will be discussed at length. Here

we note that it assumes that the deformation of the nucleus has axial

symmetry. The variety of behaviour possible for a particle coupled to

a rotor increases if the nucleus is asymmetric and in chapter 5 we shall

consider the effect of this additional degree of freedom, as calculated

for 199T1 by Meyer-ter-Vehn (Me75).

The experiments described in this thesis may now be introduced. We

have seen that 94 rotational bands have been proposed in each of the

odd-mass isotopes 191 199T1, isotopes in which deformed states might not

have been expected to occur. The 202>204Hg(d,3n)201»203T1 experiments

were conducted primarily to determine how far the % band persists as

the neutron number approaches the closed shell value N=126 and the

isotopes, presumably, become more nearly spherical. The investigation

of 199T1 using the 197Au(a,2n) reaction was designed to test the

asymmetric rotor-plus-particle predictions mentioned above in an attempt

to determine whether the deformation of the isomer in this nucleus


A measurement of the spin alignments obtained in (d,3n) reactions was required for the interpretation of data on 201T1 and 203T1. This


Chapter 2


In this chapter we shall first consider the mechanism by which the excited states of 201T1 and 203T1 were populated and then we shall detail the practical aspects of the experiments. Some of the material to be presented here will be referred to when we describe the investigation of 199T1 (chapter 5).


A general discussion of (Heavy Ion, xn) reactions has been given by Newton (Ne74b). Although the (d,3n) reactions, which we have used to study 201T1 and 203T1, and also the (a,2n) reaction by which the states of 199T1 were excited, are more accurately described as (light ion, xn) reactions, they possess many features in common with those of the (HI, xn) type. Our own discussion may therefore be based on that of Newton, although we shall take the opportunity, where it arises, to point out the special characteristics of reactions induced by light ions.

2.1.1 The Formation and Decay of the Compound Nucleus

It is useful to consider the incident ions in terms of the angular momenta they carry relative to the target nucleus. Since we are


approximate formula

E (MeV) =



where Zj, Z2 are the projectile and target charges and Aj, A 2 are their respective masses. The result is 66 MeV, corresponding to a beam energy of 73 MeV. Since the wave length X of a 73 MeV 160 ion is only 0.13 fm, it is well localised with respect to the target nucleus, and it is

reasonable to assign to each ion a classical impact parameter, r. The orbital angular momentum of the ion relative to the target nucleus is then simply (2y(E -V)}2r, where y is the reduced mass, E is the centre-of-mass energy, and V is the value of the repulsive Coulomb potential felt by the ion (V=E when the projectile and target surfaces,


considered classically, are just touching). We may estimate the £-value of the corresponding partial wave from the formula

Since the radius of the target nucleus is approximately given by 1.2 A| fm, the £-value of an 160 ion incident at surface of 164Dy, with a centre-of-mass energy 30 MeV above the Coulomb barrier, is about 30.

The classical approximation is not as good for light projectiles. Their smaller mass implies smaller linear momenta and thus longer wave

lengths at moderate energies above the Coulomb barrier. If we treat the 18-25 MeV deuterons used to bombard Hg isotopes in the present experiments


as non-relativistic = 0.026 for 25 MeV deuterons), they have X =

0.64 - 0.76 fm, five to six times greater than the wave length of the 73 MeV 160 ion. Nevertheless, we may still use the formulae above to obtain useful estimates of their angular momenta relative to various

= {2y (E -V)}^r


targets. For 25 MeV deuterons incident near the surface of 164Dy the

result is about 8 h .

Simple considerations of this kind suggest that incident ions,

particularly heavy ions, can introduce large amounts of angular momenta

into the compound nucleus. The maximum angular momentum depends on the

maximum impact parameter for which compound nucleus formation can occur.

It is likely that many of the partial waves in the region of the nuclear

surface are involved in other processes and that some of the lower

partial waves contribute to incomplete fusion reactions, in which the

projectile and target coalesce for some time, transfer clusters of

nucleons, and then separate. However, for ions incident on medium or

heavy targets at moderate energies above the Coulomb barrier, the

dominant reaction is compound nucleus formation, followed by the emission

of a number of neutrons and y-rays. Cross-sections for this reaction

are typically several hundreds of mb. Thus for 160 MeV 40Ar ions on Sn

and Te isotopes it is about 400 mb (Wa67), for 74 MeV 160 ions on 148Nd

it is about 400mb (Br75) and for 40 MeV deuterons on 187Au and 181Ta it

is about 500 mb and 1 barn respectively (Ja73, Bi74) . If we take 500

mb as a typical cross-section and simply equate it to irr2 , we obtain a

maximum impact parameter of 4 fm (assuming all collisions at smaller

impact parameters contribute to the (particle, xn) cross-section and all

those at larger impact parameters do not contribute). This is well over

half of the radius of 164Dy, for example, so our estimates of 30ft and

8ft for the relative orbital angular momenta of 150 ions and deuterons

incident at the surface of this nucleus are probably not a great deal

higher than the angular momentum input to the compound nucleus.

Not only do heavy incident ions introduce more angular momentum

into the compound system than light ions but they also produce it in a


overcome the Coulomb barrier in the case of heavy ions, at least for

those up to mass 20 or so, more than offsets the larger negative

Q-value for compound nucleus formation. Thus the excitation energy

of the compound nucleus 180W, formed in the bombardment of 164Dy by 73

MeV 160 ions, is 45 MeV, while the excitation energy of 183W formed in

the bombardment of 181Ta by 11 MeV deuterons is 22 MeV. In each example

the beam energy is just sufficient to surmount the Coulomb barrier, as

estimated from equation (2.1).

The highly excited compound nucleus will prefer to decay by neutron

emission, although fission may dominate in the case of the heaviest

compound systems. Charged particle emission is inhibited for medium

and heavy compound systems by the Coulomb barrier. Thus an a-particle

requires an energy of some 20 MeV to escape from 180W. Since the Q-value

for this process is +2.5 MeV and the Q-value for neutron emission is

probably about -8.5 MeV (Wa71), the state populated in the a-emission

will be some 9 MeV lower in excitation energy than the state populated

in neutron emission. The level densities, which increase rapidly with

increasing excitation energy, therefore strongly favour neutron emission,

although there are situations, which we shall not consider here, in

which charged particle emission may occur rather frequently.

When the compound nucleus is initially formed with a high excitation

energy, the first few neutron decays will occur between regions of very

high level densities, in which it may be reasonably assumed that the

level widths and energies are randomly distributed. Only in exceptional

circumstances will a neutron be forced to decay in one manner rather

than another. Such a circumstance may occur when the state which it

depopulates is an yrast state, which is a state of lowest energy for a

given spin. Since the excitation energy of the yrast states increases


large amount of energy must also remove angular momentum, simply because

there are no states of equal or higher angular momentum at a lower

energy. However, decays of this nature will occur rather rarely, so

that the energy spectrum of the emitted neutrons may be expected to be

statistically determined. Indeed, the neutron spectrum is found to be

an evaporation spectrum, with an average energy typically in the region

of 2 MeV and a high energy tail which may extend beyond 12 MeV.

Since the binding energies of the emitted neutrons are rather similar

(usually 7 or 8 MeV), this spectrum makes it possible to choose the

bombarding energy, and thus the excitation energy, in such a way as to

favour the population of a given residual nucleus. This is apparent

from the measured cross-sections for the 197Au(a,xn)201_XT1 reactions

shown in fig.2.1. The increase in the width of the cross-section curves

as the number of evaporated neutrons increases is due, at least in part,

to the finite width of the evaporation spectrum.

Neutrons can no longer be emitted when the excitation energy of the

compound system is less than the neutron binding energy. The remaining

excitation energy is removed by y-rays, although internal conversion

may be significant for low transition energies. Now we have seen that

the angular momentum introduced to the compound system may be very large

when heavy incident ions are used. Since the neutrons are emitted

statistically, and with an average angular momentum of only 2ft or so

(as may be verified for a 2 MeV neutron using equation (2.2)), the

residual nucleus will also have a high spin. However, y-ray studies on

states at relatively low energies show that these do not have spins

greater than about 20ft, even following reactions induced by ions such

as 35C1 and 40Ar, so a large amount of angular momentum must be removed

in the y-decays which precede the population of such states. It is


2 0 4 0 6 0 8 0 100

EQ( M e v )


are statistically emitted and do not account for the angular momentum deficit. However, these statistical decays should eventually populate states close in excitation energy to the yrast states, so that further decays must remove angular momentum. There is some evidence that a cascade down through the states close to the yrast states does occur and that it consists largely of "stretched" E2 transitions between states of spin I and 1-2. However, neither these nor the statistical y-rays appear as discrete lines in the measured spectrum. Only the decays between the few, well-separated low-lying states give rise to these.

It follows that the states which can be identified in y-ray studies of a nucleus formed in (HI, xn) reactions receive most of their population through states of higher spin, and that many of these will themselves be high spin states. When the incident projectiles are light, however, the angular momentum in the residual nucleus prior to y-decay is smaller, as might be expected from the classical estimates made earlier. A large proportion of the y-ray intensity will bypass the yrast cascade and the spin distribution of the population of the low-lying states will reflect the initial spin distribution. Thus (a,xn), (d,xn) and (p,xn) reactions are likely to be progressively less effective for the study of high spin states than (HI, xn) reactions.

Although (HI, xn) reactions have now yielded a great deal of information on high spin states, this information is necessarily restricted to states in nuclei which are deficient in neutrons. This

is partly a consequence of the increase with increasing mass of the ratio N/Z for the stable nuclei. The mass of the compound system formed by the incident heavy ion and the target nucleus is significantly larger


subsequent evaporation of neutrons enhances this deficiency. It is possible to offset this feature of the reaction by using a lighter projectile and a heavier target and in our own experiments on 201T1 and

203T1, which lie close to the line of nuclear stability, it proved necessary to use deuterons in conjunction with Hg targets. Since the purpose of the experiments was to populate high spin states, namely those of a ^ rotational band, this must be seen as something of a disadvantage.

2.1.2 Gamma-Ray Spectroscopy

It is a characteristic of (HI, xn) reactions that the input angular momentum is sufficiently large that the compound nuclear spins are

highly aligned in a plane perpendicular to the direction of the incident beam. This alignment is largely maintained in the statistical evaporation of the neutrons and y-rays and is only disturbed by small amounts in the yrast cascade of stretched transitions, so that the spins of the low- lying states are also highly aligned. It is therefore possible to gain spectroscopic information on these states by measuring the angular distributions of the y-rays which depopulate them. However, when a light incident ion is used, the input angular momentum is much smaller and the alignment in the residual nucleus less pronounced, with the consequence that the angular distributions are potentially less

informative. Values of the degree of alignment obtained in a number of (d,3n) reactions are given in Appendix 1, where this matter is discussed in more detail.

Further spectroscopic information can be obtained by measuring y-ray yields as a function of beam energy. It is clear from fig.2.1 that the cross-section for (particle, xn) reactions can change rapidly for


to the de-excitation of a particular residual nucleus by observing its yield as a function of beam energy. Such an observation may also give information on the spin of the level which the y-ray de-excites (Ne68). As the beam energy increases, the angular momentum that can be introduced

into the compound nucleus also increases. Furthermore, the energies of the yrast states increase with increasing spin, with the consequence that the energy thresholds for the population of the higher spin states are greater than for the lower spin states. The population of the higher spin states in the compound nucleus therefore increases relative

to that of the lower spin states with increasing bombarding energy. When light projectiles are used this variation is reflected in the population of the states at low excitation energies in the residual nucleus and a measurement of y-ray excitation functions can therefore provide very useful information on the spins of these states, as is clear

from fig.2,2. When heavier ions induce the reaction, and most of the y-ray intensity cascades through the yrast region, the effect may be

less dramatic. In all cases the population of the low-lying states depends in detail on the preceding sequence of decays and excitation

function data should be interpreted with care.






























( d,3n) 164Er







-• ---- ---

-• --- -• --- *

4 ^ 2


energy MeV

Fig.2.2 Some relative y-ray excitation functions, measured for states

populated in (d,3n) reactions. The residual nuclei are

rotational and the states are members of their ground state

rotational bands. The excitation functions are normalised to

the yield of the 4-*2 y-ray at each bombarding energy and to


It is not always necessary to vary the beam energy to obtain spectroscopic information from the level populations. When there are levels of the same spin available for population by a y-ray in the de-excitation of the residual nucleus, the energy dependence of the transition probability will tend to favour the population of the yrast state. It is therefore possible to draw conclusions concerning level spins from the observed populations, since the levels are mostly fed through levels at higher excitation energies. Thus, if two states in the final stages of the de-excitation process are equally populated and one is several hundreds of keV above the other in excitation energy, it is unlikely that they have the same spin, unless the upper state has particular properties which result in its preferential population. The fact that the residual nucleus is formed in a wide variety of states at a large number of different excitation energies means that selective population of this kind should occur only rarely.

Since the yrast states are favoured in population it is less easy to detect non-yrast states. We shall consider how to increase the probability of detecting such states in chapter 5.


The excited states of 20*T1 and 20 3T1 were populated in (d,3n)


Some features of the experimental arrangement are shown in fig.2.3. A quadrupole lens was used to focus the beam through an aperture 6 mm in diameter in a Pb collimator. The collimator was 4 mm thick, so the radiation level in its vicinity was very sensitive to the amount of beam

intercepted. A counter placed close to it could therefore be used to monitor this, providing an effective alternative to the available current

integrator, which was inadequate at the very low currents used.

Fig.2.3 The experimental arrangement for the

202,20LfHg (d, 3n) 201,2 0 measurements. The diagram is not drawn to scale.

It was shown that, when the counting rate was minimised, the diameter of the beam spot at the target position was 2 mm. The collimator and

the target were optically aligned before each experimental run. A 4 mm thick Pb disc was used to stop the beam 2 m beyond the target and the y-ray detectors were shielded from the disc by a beam dump containing a large mass of paraffin and borax.

The targets consisted of 2 mg cm 2 of isotopically enriched 202Hg (76.8% enrichment) and 201+Hg (92.6% enrichment), in the form of oxide powders glued to 1.3 mg cm 2 mylar backings. They therefore contained


which had a volume greater than 60 cm3, were relatively insensitive to the mainly high energy y-rays resulting from reactions on light elements.

In some (d,3n) studies on rare earth targets a comparison was made between the spectra obtained from rolled metal foils and oxide powders

supported in the manner described above. There was only a small improvement in quality when the metal foils were used.

The energy loss of the deuteron beam in the targets can be estimated from the tables of Northcliffe and Schilling (No70) . For 24 MeV

deuterons it is only about 0.1 MeV. A much thicker target could therefore have been used before serious competition between the (d,3n) and (d,2n) reactions occurred. However, the thickness was limited by the dependence of the resolution of the y-ray detectors on their counting rates. The resolution was found to deteriorate at rates > 10 KHz.

Gamma-ray spectra were taken with three Ge (Li) detectors in the course of the experiments. The largest of these was a 60 cm3 coaxial detector, which was suitable for the detection of the higher energy y-rays. An 11 cm3 planar detector was less sensitive to these and

therefore gave lower Compton scattering backgrounds. Its smaller volume and the uniformity of the electric field made it suitable for the timing measurements described in section 2.3.4. The measured resolution (FWHM) of each of these detectors was 1.8 keV at a y-ray energy of 122 keV. A 3.3 cm3 planar detector, fitted with a 0.13 mm Be window, was used for the study of y-rays with energies below 100 keV. Its resolution was found to be 0.8 keV (FWHM) at 122 keV.


et al

(Le67) taken as standards.

In order to obtain accurate energies for the y-rays emitted in the reactions, the spectra were measured simultaneously with the spectrum from a 152Eu source. (A simultaneous measurement allows errors arising from the counting rate dependence of the amplifier gains to be avoided.) The energies of the 152Eu decay y-rays are known very accurately and the values used, which were those of Riedinger

et al

(Ri70), have recently been confirmed by the precise measurements of Borchert (Bo75). The calibration of the 3.3 cm3 detector in the energy region below 100 keV was made using the known energies of the T1 and Hg X-rays and confirmed with 57Co, 241Am and 133Ba sources.


A number of standard techniques in y-ray spectroscopy were used to assign y-rays appearing in the spectra to 201T1 and 203T1, to construct level schemes for these nuclei and to obtain information on the spins of the decaying states. These techniques are well documented in the

literature and we shall concentrate here only on the relevant experimental details. The analysis of the data and the results obtained will be the subject of chapter 3.

We have already commented on the fact that the bombarding energy can be chosen to favour the population of a particular residual nucleus in (particle, xn) reactions. The energy most convenient for the


2.3.1 The y~y Coincidence Experiment

A very powerful technique for both assigning y-rays to a particular nucleus and for constructing level schemes is the measurement of the coincidence relationships between the y-rays. The experimental geometry and the fast-slow coincidence circuitry used in the present measurement are shown in fig.2.4.

In order to maximise the real-to-random coincidence ratio a narrow coincidence chamber was used. The chamber was of stainless steel with windows 0.5 mm thick. When the detector faces were placed against these they were only some 2.5 cm from the centre of the target.

The three parameters associated with each event, defining the energies of the y-rays observed and their mutual time relationship, were stored event-by-event onto magnetic tape for subsequent analysis. Conversion gains of 4096, 4096 and 512 channels were used for the two y-ray spectra and the time spectrum respectively. The resolution of the coincidence peak in the totalised time spectrum was 12 ns (FWHM) and the real-to-random ratio was approximately 7:1.

2.3.2 Gamma-Ray Angular Distributions

The angular distributions of the 201T1 and 20 3T1 y-rays were measured at beam energies of 24 and 25 MeV. Observations were made with the 60 cm3 detector at six angles between 90° and 153° and at a distance from the target of 20 cm.


+■> CD



•H CD £

' 5

/ z

a C/D w _J ID Q O 5 O t-< UJ ® E 5g sS

_i co

UJ >- h— O QC UJ a UJ E K *

t * ♦ lO « K«I to CM ev

♦ t t t

Oj a g CM > UJ E— CO o CM T3 £ aJ o CM •H CD r-H o D C CD rP +-> c O (/) +-> e •H fn CD S* CD CD O p CD ■H O C •H o o >-CD rP +-> fn O M -i X fH +-» •H 3 O Eh •H U O •H P o h


succession of pulses, they had to be measured using a beam-related

technique. The method adopted was to compare, for each detector, the

number of signals at the output of the linear amplifier with the number

of counts in the measured spectrum. A single channel analyser was used

to ensure that all of the output pulses had heights within the ADC

conversion range.

A 152Eu source was placed at the target position and its yield was

measured at each of the six angles used. A correction could then be

made for any effects arising if the target were not at the centre of

rotation of the detector and for any departure of the target chamber

from cylindrical symmetry. The chamber walls were of perspex 6 mm thick.

Gamma-ray angular distributions are often characterised in terms

of the coefficients A 2 and A 4 in the formula

W (0) = 1 + A 2P2 (cos 0) + A 4P4 (cos 0) (2.3)

where P2 (cos 0) and P4 (cos 0) are Legendre Polynomials. For y-rays

following (particle, xn) reactions A4 is usually rather small. Furthermore,

P 2 (cos 0) has zeros at 55°, 125°, 235°, ... , so if the detector is

placed at one of these angles, rather good estimates of the y-ray

relative intensities can be made. This is the reason why a detector

angle of 125° was chosen in three of the following experiments.

2.3.3 Gamma-Ray Relative Excitation Functions

These were measured in order to aid in the assignment of y-rays

to 201T1 and 203T1 and to provide information on the spins of the levels

they depopulate (see section 2.1.2). Beam energies of 18, 20, 22, 24


detector at an angle of 125° to the beam direction.

2.3.4 The d-y Delay Experiment

The ANU cyclotron allows the extraction of one orbit at a time

from the dees ("single turn extraction") . This makes it a suitable

device for timing purposes because the decay of a y-ray can be measured

between well-defined beam pulses. These had a duration of some 3 ns

and occurred every 70 ns. Slits within the cyclotron dees were used to

minimise the time spread of the beam.

The electronic circuitry used differed from that shown in fig.2.4

in the omission of the 60 c m 3 detector-preamplifier combination and its

associated slow circuitry, and in the replacement of the fast signal

derived from this combination by a signal from the rf oscillator of the

cyclotron. The 11 cm3 planar detector, placed at an angle of 125° to

the beam direction, was used to observe the y-rays. This detector was

used in preference to the 60 c m 3 coaxial detector because of its superior

timing characteristics. A FWHM resolution of 8.6 ns at 169 keV and

5.5 ns at 436 keV was obtained. The time spectrum was calibrated by

switching in known delays and the time and energy parameters were stored

event-by-event onto magnetic tape for subsequent analysis. The

conversion gains were 512 and 4096 channels respectively.

2.3.5 The Low Energy y-Ray Spectrum

An analysis of the y-y coincidence relationships (see section 3.2.2)

implied that a transition of energy 33.4±0.2 keV de-excited one of the

levels of 203T1. A search for a y-ray of this energy was made with the

3.3 c m 3 Be-windowed Ge (Li) detector, which was the only detector


excessive attenuation of low energy y-rays. A 33.4±0.1 keV y-ray and also a 31.110.1 keV y-ray were detected when the 204Hg target was

bombarded. In order to show that these were likely to be 20 3T1 y-rays, a study was made of the spectrum resulting from the bombardment of the 202Hg target, which had been manufactured in the same way. The two y-rays were not detected.

2.3.6 The n-y Coincidence Experiment

Coincidences were measured between the neutron events detected in an NE213 liquid scintillator at 30° to the beam direction and the y-ray events in the 60 cm3 Ge (Li) detector at 125°. The y-ray flux at the scintillator was attenuated with a 3 cm Pb absorber and the neutrons distinguished from the remaining y-rays by pulse shape discrimination. The y-rays in fast coincidence with the neutrons were collected for analysis.


Chapter 3


This chapter is divided into three sections. In the first the

y-rays assigned to 201T1 and 203T1 are presented with their measured

properties, in the second level schemes for the two nuclei are deduced

and in the third spin assignments are made.


The y-ray singles spectra resulting from the bombardment of the

202Hg and 204Hg targets are shown in fig.3.1. The spectra resulting

from the population of final odd-mass nuclei in (particle, xn) reactions

are usually more complex than in the case of final even-even nuclei

because of the increased level density. Additional complexity in the

present spectra arises from the inelastic scattering of deuterons on the

Hg, as can be seen from the number of peaks marked (d,d') in the figure.

Gamma-rays from the odd-odd nuclei 202T1 and 204T1, formed in (d,2n)

and (d,4n) reactions, also appear, as do peaks resulting from the

inelastic scattering of neutrons both on the iron in the beam line (the

847 keV 56Fe peak) and on the germanium in the detector (the 596 keV

74Ge and 690 keV 72Ge peaks). The presence of large amounts of carbon

in the targets is evidenced by the 169 keV 13C y-ray emitted following

the 12C(d,p) reaction.

The y-rays which could be assigned to the nuclei 201T1 and 20 3T1

are listed with their measured properties in tables 3.1 and 3.2. Where

the assignments are not definite the y-ray energies appear within






































TABLE 3.1 Transitions in 201T1

E (keV)

Y IY a2 A4 *D T^(ns)

123.3 6.310.9

155.4 4.6+0.7

166.9 9.1 + 1 .4

319.0 100 -0.4 5 U 0 . 013 -0.04510.018 22 2.4+ 3 '8 -0.8 331.2±0.2 257126 0.012+0.015 -0.008+0.018 184 >60 333.010.2 76.718.0 -0.383+0.029 0.05210.046

361.3 21.311.9 -0.09910.026 0.02610.038 0

390.5 31.3+3.2 -0.40710.026 0.010+0.037 0

(426.9+0.3) 9.1 + 1.9 0.281+0.053 -0.00210.065 443.2

468 .410.3

27.H3.2 6.2H.4

0.16210.010 0.00210.015 23 2 9+1,9 -0.5

(493.9) 30.9+4.3 -0.20310.018 0.05510.026 0

588.3a^ 19U9 0 0 191 >60

598.010.5 12.013.0

652.010.4 22.412.5 0.20410.050 -0.06210.077 723.910.2^ 11 .712.3 0.32910.150

(749.210.3) 9.1 + 1 .8 785.310.3 9.2H .9

803.6 52.613.3 0.136+0.019 -0.05010.044 0

a) This y-ray is known to depopulate the 2.1 ms isomeric state. It was shown to be isotropic by the monitor normalisation method

and has been used to provide the normalisation for the remaining y-ray angular distributions.


TABLE 3 . 2

T r a n s i t i o n s i n 203T1

E (keV)

Y IY a2 a4 l D T^Cns)

( 3 1 . 1 ) 0 . 3 1 0 . 0 6

( 3 3 . 4 ) 0 . 5 1 0 . 0 7

1 2 3 . 5 1 0 . 3 1 . 4 1 0 . 2

1 4 3 . 6 8 . 7 + 0 . 3 - 0 . 1 0 4 + 0 . 0 1 8 - 0 . 0 2 2 + 0 . 0 2 8

9 0 + 1 - 9 - 2 . 4 2 3 1 . 9 5 8 . 7 + 2 . 2 - 0 . 1 0 4 + 0 . 0 0 5 0 . 0 0 3 + 0 . 0 0 9 2 5 . 6

2 6 5 . 0 1 0 . 2 3 . U 0 . 4 - 0 . 1 8 7 + 0 . 0 6 0 - 0 . 1 2 7 + 0 . 0 8 6

7 ' 6 - 2 . 1 2 7 9 . 1 100 0 . 1 4 2 + 0 . 0 0 8 - 0 . 0 0 2 + 0 . 0 1 3 2 3 . 5

3 0 3 . 6 1 0 . 2 3 . 1 + 0 . 7

3 2 8 . 1 1 0 . 2 6 . 3 1 0 . 4 - 0 . 1 4 2 + 0 . 0 2 6 0 . 0 2 6 + 0 . 0 3 7

3 5 0 . 2 1 0 . 3 < 8 . 9 H .4

3 6 2 . 9 1 0 . 2 4 . 8 1 0 . 5 - 0 . 2 9 7 + 0 . 0 3 7 - 0 . 0 1 2 1 0 . 0 5 9

3 8 6 . 9 1 0 . 3 5 . 0 1 1 . 1

401 .4 1 6 . 6 + 0 . 9 - 0 . 1 2 3 + 0 . 0 2 5 - 0 . 0 2 0 1 0 . 0 4 0

5 0 3 . 8 1 0 . 2 3 . 8 1 1 . 3

5 3 3 . 4 8 . 3 1 0 . 6 - 0 . 0 6 8 1 0 . 0 1 9 - 0 . 0 4 9 + 0 . 0 2 8

5 3 7 . 2 7 . 3 1 0 . 6 0 . 1 9 5 1 0 . 0 2 9 - 0 . 0 5 7 1 0 . 0 4 1

00 1 +






5 8 8 . 3 4 0 . 1 + 1 . 6 0 . 1 3 7 + 0 . 0 0 8 - 0 . 0 2 4 1 0 . 0 1 1 2 1 . 3

6 8 0 . 7 1 0 . 2 4 . U 0 . 5

c + 2 . 3 6 ’ 5 - 3 .5 7 9 5 . 0 5 4 . 6 + 2 . 3 0 . 1 4 0 1 0 . 0 0 7 - 0 . 0 1 0 + 0 . 0 1 0 1 3 . 9


otherwise stated. With the exception of the 31.1 keV and 33.4 keV

203'n y-rays, which were discussed in section 2.3.5, assignments were

made on the basis of y-y and n-y coincidence relationships and y-ray

relative excitation functions.

The relative intensities I in tables 3.1 and 3.2 are given for a

beam energy of 24 MeV and where possible are corrected for the angular

distribution coefficients A2 and A4. These were obtained from a least

square fit of the normalised intensities W(0) to the formula

wee) =


+ A2P2(cos 0) + A4P4(cos 0) ( 3 . 1 )

and are not listed where the y-rays were too weak or insufficiently

resolved for their extraction from the data. In these cases, relative

intensities are derived from other singles data, taken at 125° in most

cases. The errors at this angle are small, as explained in section

2.3.2. Where the angle was not 125°, the errors in the relative

intensities include estimated errors for angular distribution effects.

Errors in all the relative intensities include those in the detector

relative efficiencies.

The information derived from the d-y delay measurements is also

listed. As a first step in the analysis of these the magnetic tapes

were sorted to yield the energy and time spectra summed over all the

events . Windows were then set on the peaks of interest in the energy

spectrum and the time spectra associated with these were obtained. The

effect of the background beneath a peak was approximately corrected for

by subtracting the time spectrum, appropriately normalised, for a

background close to it. Both prompt components, which we define as

those with half-lives Ta of less than a few nanoseconds, and delayed


can be seen from the examples in fig.3.2. For the delayed components,

the half-lives were obtained by fitting an exponential to the time

spectrum. The results were checked by integrating peaks in the energy

spectra which were projected from successive regions of the totalised

time spectrum. The intensities of the delayed components, 1^, were

calculated using the formula

N = A N (1 - e ~ Xx)



e - e


where AN is the number of transitions occurring in the time interval

t i-t2 , t is the cyclotron period and A = (log 2 ) / % .

e -g

The relative excitation functions for y-rays which were assigned

to 201T1 and 203T1 are shown in fig.3.3. We mentioned in section 2.1.2

that excitation function data can aid in the assignment of level spins

and the curves shown in the figure will be used for this purpose in

section 3.3.

The y-y coincidence relationships were determined in the following

way. The data tapes were sorted to yield the totalised time spectrum

and the sum coincidence spectrum for each detector. These are shown in

f ig.3.4 for the nucleus 203T1. Windows were then set on the time peak

and on the peak of interest in one of the sum coincidence spectra. The

spectrum of events in the other detector associated with the events

within these windows could then be obtained. Background subtractions

were made as in the analysis of the d-y delay data. A window on the 279

keV peak in the sum coincidence spectrum of the planar detector is

shown in fig.3.4, as are two windows suitable for making a background

correction. The effect of random coincidences could be investigated by

setting a window on the random part of the time spectrum. When all






















M o p u i M p u n o j 6 > ( 3 e q a i q i s s o d

M o p u iM p u n o j 6 > * o e q a i q i s s o d

00 (O sf CJ O


TABLE 3.2T r a n s i t i o n s  in 203T1
TABLE 3 2T r a n s i t i o n s in 203T1. View in document p.42
TABLE 3.3Coincidences in 201T1
TABLE 3 3Coincidences in 201T1. View in document p.48
TABLE 3.6 Mixing Ratios
TABLE 3 6 Mixing Ratios. View in document p.58
Fig. 4.2
Fig 4 2 . View in document p.72
TABLE 4.1Calculated and Experimental Reduced Transition
TABLE 4 1Calculated and Experimental Reduced Transition . View in document p.91
TABLE 4.3C alculated and Experimental Single Hole Strengths and
TABLE 4 3C alculated and Experimental Single Hole Strengths and . View in document p.93



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