Beta Decay Beta Decay

Beta Decay Beta Decay

Allowed decays Allowed decays Fermi transitions Fermi transitions

†

J_f M_fT_fT_{0 f} T_m J_iM_iT_iT_0i = T_i(T_i + 1) - T_0i(T_0i m1)dJ_iJ_fd_MiMfd_TiTfd_{T0 im1T0 f}

In reality, isospin is violated by the electromagnetic force, but the violation is weak.

†

J_f = J_i (DJ = 0)

T_f = Ti ≠ 0

(

)

T_{0 f} = T_0i m1 DT( 0 = 1)

Dp = 0 no parity change

T₊ has rank unity!

Gamow

Gamow-Teller transitions-Teller transitions

The matrix element strongly depends on the structure of the wave function!

†

DJ = 0,1 but J_i = 0 Æ J_f = 0 forbidden DT = 0,1 but T_i = 0 Æ Tf = 0 forbidden T_{0 f} = T_0i m1 DT( 0 = 1)

Dp = 0 no parity change

The absolute values of GT matrix elements are generally smaller than those for Fermi transitions.

†

fT = const

F

+ g

GT

squared matrix elements

Beta Decay Beta Decay

Forbidden transitions Forbidden transitions

Forbidden transitions involve parity change and a spin change of more than one unit. They come from the higher-order terms in the expansion of electron and neutrino plane waves into spherical harmonics. Forbidden decays are classified into different groups by the L-value of the spherical harmonics involved. The selection rules for the Lth-order forbidden transitions are:

†

DJ = L or L ± 1, Dp = (-1)^L

Experimental log fT values

Beta Decay Beta Decay

electron capture processes electron capture processes

Electron capture leads to a vacancy being created in one of the strongest bound atomic states, and secondary processes are observed such as the emission of X- rays and Auger electrons. Auger electrons are electrons emitted from one of the outer electron shells and take away some of the remaining energy.

Capture is most likely for a 1s-state electron. The K-electron wave function at the origin is maximal and is given by

†

y

p

Zm_ee² h² Ê

Ë Á Á

ˆ

¯

˜ ˜

3/ 2

†

W

= E

M

g

p

_h

^c

Zm

e

h

Ê

Ë Á Á

ˆ

¯

˜ ˜

3 The electron capture probability is thus given by:

Beta Decay Beta Decay

the neutrino the neutrino

One of the most pervasive forms of matter in the universe, yet it is also one of the most elusive!

inverse beta processes

Shortly after publication of the Fermi theory of beta decay, Bethe and Peierls pointed out the possibility of inverse beta decay (neutrino capture):

†

Z

AX_N +n_eÆ_{Z +1}^AX_N-1+ e^-

Z

AX_N +n _eÆ_{Z -1}^AX_{N +1} + e⁺

extremely small cross sections!

†

p + n _e Æ n + e⁺

Let us first consider

†

s_c^=W_{i Æ f} ^V

c = 2p^V

h M_fi ² dn

cross section dE

neutrino flux

†

E_n

e /m_ec² E

e⁺ /m_ec² s /10^{-4 4}cm²

4.5 2.0 8

5.5 3.3 20

10.8 8.3 180

†

l = 1 n s

mean-free path

number of nuclei per cm³

For protons in water n~3 10^22.

This gives the mean-free path of 3 10²⁰ cm or ~300 light years!

Beta Decay Beta Decay

the neutrino detection the neutrino detection

In 1930 Wolfgang Pauli proposed a solution to the missing energy in nuclear beta decays, namely that it was carried by a neutral particle This was in a letter to the Tubingen congress. Enrico Fermi in 1933 named the particle the "neutrino" and formulated a theory for calculating the simultaneous emission of an electron with a neutrino. Pauli received the Nobel Prize in 1945 and Fermi in 1938. The problem in detection was that the neutrinos could penetrate several light years depth of ordinary matter before they would be stopped.

In 1951 Fred Reines at Los Alamos thought about doing some real challenging physics problem. In a conversation with Clyde Cowan they decided to work on detecting the neutrino. Their first plans were to detect neutrinos emitted from a nuclear explosion.

Realizing that nuclear reactors could provide a neutrino flux of 10¹³ neutrinos per square centimeter per second, they instead mounted an experiment at the Hanford nuclear

reactor in 1953. The Hanford experiment had a large background due to cosmic rays even when the reactor was off. The detector was then moved to the new Savannah River nuclear reactor in 1955. This had a well shielded location for the experiment, 11 meters from the reactor center and 12 meters underground. The target was water with CdCl_2 dissolved in it. The positron was detected by its slowing down and annihilating with an electron producing two 0.5 MeV gamma rays in opposite directions. The pair of gamma rays was detected in time coincidence in liquid scintillator above and below the water by photomultiplier tubes detecting the scintillation light. The neutron was also slowed by the water and captured by the cadmium microseconds after the positron capture. In the capture several gamma rays were emitted which were also detected in the scintillator as a delayed coincidence after the positron's annihilation gamma ray detection. .

Beta Decay Beta Decay

the neutrino detection (cont.) the neutrino detection (cont.)

The rarity of neutrino capture is shown in their signal rate, which was about three events per hour in the entire detector. The signal to background ratio was about four to one. Thus in 1956 was born the rich and continually exciting field of experimental neutrino physics, as discussed in other articles in this newsletter. This discovery was recognized by honoring Frederick Reines with the Nobel Prize in 1995. Clyde

Cowan died in 1974….

Original papers:

• “Detection of the Free Neutrino: A Confirmation", C.L. Cowan, Jr., F. Reines, F.B.

Harrison, H.W. Kruse and A.D. McGuire, Science 124, 103 (1956).

• "The Neutrino", Frederick Reines and Clyde L. Cowan, Jr., Nature 178, 446 (1956).

• "Neutrino Physics", Frederick Reines and Clyde L. Cowan, Jr., Physics Today 10, no. 8, p.12 (1957).

Beta Decay Beta Decay

double beta decay double beta decay

†

f V_int i = f V n n V i E_i - E_n

n

Â

second order process

†

Z

A

X

Æ

Y

+ e

+ e

+ n

+ n

summary of selected double beta-decay results

Typical lifetimes are of the order of 10²⁰ years extraction of

the daughter nuclei (Z+2) from the parent (Z) in an old ore

Seen in: ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr,

100Mo, ¹¹⁶Cd, ¹⁵⁰Nd,…

Beta Decay Beta Decay

double beta decay (cont.) double beta decay (cont.)

It was suggested that neutrino can be identical or different to its charge conjugate:

†

Cu ≡ u = u (Majorana particle)

†

Cu ≡ u ≠ u (Dirac particle)

Majorana particles appear in a natural way in GUT theories that unify the strong and electroweak interactions with the possibility that the lepton number is no longer conserved, since now the emitted antineutrino could be absorbed as neutrino:

†

Z

A

X

Æ

Y

+ e

+ e

2nbb

0nbb

two-electron spectrum

The estimated transition probability for the neutrinoless decay is more than 10⁵ shorter than the “normal” double-beta decay

Beta Decay Beta Decay

double beta decay (cont.) double beta decay (cont.)

The difference between Majorana and Dirac neutrinos were tested by Davis in 1955. The reaction:

†

n _e + n Æ p + e^- (n Æ p + e^- +n _e)

has not been observed. This can be understood in light of parity violation by weak interaction. Indeed, the inverse reaction needs different helicity:

†

n Æ p + e^- +n _e(R) n(L) + n Æ p + e^-

By the same token, the neutrinoless double-beta decay is forbidden, even if neutrino has a Majorana character! Note, however, that for the massive particle helicity is not a fixed quantum number!