Nuclear Structure and Reactions

Nuclear Structure and Reactions

Witold Nazarewicz

Resolution Meeting, Long Range Plan 2014-2015

•  What has been accomplished since 2007?

•  What can be done over next 5 and 10 years?

•  What major discoveries will emerge?

•  What major new investments are needed?

o  Major facilities

o  Major items of equipment

o  Major focus of research resources

•  Recommendations from Town Meetings

•  Other recommendations for consideration

The Nuclear Landscape and the Big Questions (NAS report)

•  Where do nuclei and elements come from?

•  How are nuclei organized?

•  What are practical and scientific uses of nuclei?

To Understand, Predict, and Use…

Revolution due to major advances in accelerator technology, experimental

techniques, analytic theory, and computing.

This has led to a shift from purely phenomenological models to nuclear theory grounded in the Standard Model.

Today, we are constructing a roadmap that will lead to a predictive model of nuclei.

DFT CI ab initio

LQCD

How to explain the nuclear landscape from the bottom up?

Theory revolution

THE HOYLE STATE DECAY AND FUTURE OPPORTUNITIES Hoyle-state E0 form factor

0 1 2 3 4

10^-4 10^-3 10^-2 10^-1

k (fm^-1) ftr(k)

VMC GFMC Experiment

0 0.2 0.4

0 1 2 3 4 5 6

k² (fm^-2) 6 Z ftr(k) / k2 (fm2)

The GFMC E0 form factor (solid red) is significantly larger than the starting wave function result (open red) and in excellent agreement with data (black stars).

Extrapolation to k = 0 (inset) gives the B(E0); again the GFMC result agrees well with experiment.

• Calculation of other¹²C states and their electromagnetic transitions is underway

• Also computing electroweak response of¹²C ground state (see Carlson’s contribution Neutrino-nucleus scattering).

Hoyle state E0 form factor with Quantum Monte Carlo

Nuclear magnetic moments from Lattice QCD

Resolution

Coupled cluster description of binding energies and radii

Who could have predicted this 20 years ago? ^{45 50 55 60 65}

E_c.m. (MeV) 10^-4

10^-3 10^-2 10^-1 10⁰ 10¹ 10²

fusion (mb)

E_c.m. = 55 MeV, TDDFT Experiment

Fusion cross sections from TDDFT

48Ca+⁴⁸Ca

What has been accomplished since 2007?

(see backup slides for a more inclusive list)

• New  experimental  insights  make  it  it  necessary  to  rewrite  nuclear  structure   textbooks.  Data  from  the  most  exo:c  nuclei  proved  crucial.  

• Quan:ta:ve  ab-­‐ini:o  nuclear  structure  &  reac:on    calcula:ons:  the  first  

descrip:on  of  the  Hoyle  state  in  ¹²C,  explana:on  of  the  useful  half-­‐life  of  ¹⁴C  crucial   for  carbon  da:ng;  n+t  cross  sec:on  predic:ons  for  iner:al  confinement  fusion;  

explana:on  of  g_A  quenching;  descrip:on  of  ⁴⁸Ca;  descrip:on  of  neutrino-­‐nucleus   interac:ons;  and  impact  of  3N  forces  on  the  neutron  star  radius.  

• Discovery  of  elements  114-­‐118    and  confirma:on  of  existence  of  other  superheavy   nuclei.  Evidence  for  region  of  enhanced  stability.  Chemistry  of  Z=106  and  114.  

• Superallowed  beta-­‐decays  confirm  unitarity  of  CKM    matrix  to  an  unprecedented   level  of  precision.  Confirma:on  of  octupole  correla:ons  in  complex  nuclei  involved   in  EDM  measurements.  

New Closures N = 32 & 34

Revision of nuclear structure textbook knowledge

The ab-initio frontier: neutron-rich calcium isotopes

Neutron number 38

S 2n (MeV)

36 34

32 30

28 2 4 6 8 10 12 14 16 18

Experiment MBPT CC CI (KB3G) CI (GXPF1A)

Ca

2 3

Theory Experiment

34 32

E(2+ ) (MeV) 1

(a)

(b) Nuclear Forces

from χEFT

NN 3N 4N

(2011) (2006) derived in (2002)

Extrapolations are tough Unique data

optimized in 2014

Reproduction of known data

Prediction of weak charge f.f.

What are the limits of atoms and nuclei? Do very long-lived superheavy nuclei exist in nature?

Structure of nuclei at the limit of mass and charge (Coulomb frustration) Cosmic origin of superheavy nuclei

Very relativistic atoms with Zα → 1

155

Neutron number

Half-life, T(s)

160 165 170 175

118 117

116 114

112

112 113

110 113

110

111

111

111

115

10^-6 180 10^-4 10^-2

10^-4

10^{0 1 s} 1 min

1 ms 10²

          

       







          

      

       

      

     

     

    

   

   

 







  





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•  Around 30 new superheavy isotopes found since 2007

•  Z=114 (Fl) and 116 (Lv) named

•  Z=117, 115 confirmed

•  Unique spectroscopic data above Z>102

•  Chemistry of Z=106, 114

Shell energy

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nuclear meson decay 20

30 40

10

NUMBER OF NEUTRONS

20 30 40 50 60

10

0 ,1

0 ,1⁺

+

BR t1/2

Q_EC

Superallowed ! emitters

NUMBER OF PROTONS

Superallowed Fermi 0

→0

β -decay studies

Impressive experimental effort worldwide

+ Theory!

"It is exceedingly difficult to make predictions, particularly about the future” (Niels Bohr)

Some  An:cipated  NS  Greatest  Science  Hits:  next  5  years  

•  Accessing  the  neutron  drip  line  up  to  A=40  to  test    models  of  nuclear  binding  with  a  strong   focus  on  long  isotopic  chains,  in  par:cular  Z=8,  20,  28,  40.  The  existence  (non-­‐existence)    of  

28O  will  be  confirmed.  Data  on  very  neutron-­‐rich  Ca  isotopes  will  test  ab-­‐ini:o,  DFT,  and   reac:on  models,  and  help  quan:fying  uncertain:es  for  extrapola:ons.    

•  We  will  make  first  direct  Z  and  A  iden:fica:on  and  chemical  characteriza:on  of  superheavy   elements  with  Z  ≥  113.  New  elements  Z=119  and  120  will  be  discovered.  

•  Significant  regions  of  the  r-­‐process  nuclei  will  be  accessible  for  the  first  :me  for  mass  and   decay-­‐property  measurements,  providing  experimental  informa:on  to  test  many  cri:cal   aspects  of  r-­‐process  models.  

•  We  will  improve  limits  on  the  neutron-­‐ma`er  equa:on  of  state  and  3N  forces  from   measurement  of  the  size  of  weak  radius  in  ²⁰⁸Pb  and  ⁴⁸Ca  skins,  and  electric  dipole   polarizability  in  neutron-­‐rich  nuclei.  

•  We  will  compute  nuclear  matrix  elements  for  0νββ  decay  in  complex  nuclei  and  quan:fy   uncertain:es  by  tes:ng  models  against  available  data.  

Some  An:cipated  NS  Greatest  Science  Hits:  next  10  years  (first  5  years  with  FRIB)  

•  Delinea:on  of  the  neutron  drip  line  up  to  A=120  to  test    models  of  nuclear  binding.    Key  

isotopic  chains  will  be  measured  from  proton  drip-­‐line  to  neutron  drip-­‐line,    revealing  the  N/Z   dependence  of  the  nuclear  force.  In  par:cular,  the  spectroscopy  of  ⁶⁰Ca  will  be  carried  out  at   FRIB  with  GRETA  and  HRS.      

•  Neutron  pairing  will  be  explored  using  transfer  reac:ons  in  nuclei  with  extreme  neutron  skins.  

•  We  will  know  whether  there  is  an  experimental  path  to  very  long-­‐lived  superheavy  nuclei.  

•  Key  regions  of  the  r-­‐process  will  be  accessible  for  the  first  :me  for  mass  and  decay-­‐property   measurements.  In  par:cular,  significant  data  will  be  obtained  around  and  above  ⁷⁸Ni  and  

132Sn,  and  in  the  region  of  N=126  nuclei  below  Pb  in  atomic  number.    

•  A  new  expanse  of  nuclear  territory  with  Z≳N,  at  and  beyond  the  proton  drip-­‐line,  will  become   accessible  up  to  ¹⁰⁰Sn.  New  phenomena  will  be  studied,  such  as  superallowed  Gamow-­‐Teller   decays,  the  role  of  proton-­‐neutron  pairing,  and  alpha  clustering  at  the  nuclear  surface.  

•  Key  light-­‐ion  fusion  reac:ons,  involving  composite  projec:les,  will  be  computed  ab-­‐ini:o.  

Spectroscopic-­‐quality  nuclear  energy  density  func:onal  will  be  developed,  rooted  in  chiral   inter-­‐nucleon  interac:ons  and  op:mized  to  data  on  nuclei  with  extreme  N/Z  ra:os,  ab-­‐ini:o   theories,  and  neutron  star  observa:ons.  

16 ment. Bands with these properties have been reported

in both ²²⁴Ra and ²²⁶Ra [Wol93, Coc97]. Furthermore, a pioneering Coulomb excitation measurement was carried at REX-ISOLDE with ²²⁰Rn and ²²⁴Ra radioac- tive beams [Gaf13], which provided the E2 and E3 in- trinsic moments for the two nuclei. The data provide evidence for stronger octupole deformation in ²²⁴Ra and the results enable discrimination between some of the available calculations. Inverse-kinematics, barrier- energy Coulomb excitation, with GRETA for -ray detection, is best suited to search for the regular band structures that serve as a fingerprint for static octupole deformation. With multiple Coulomb excitation at beam energies near the Coulomb barrier, the nucleus can be excited to states of relatively high spins: spins as high as 36 have been observed in ²³²Th and ²³⁸U, for example. In the near-term, with GRETINA at AT- LAS/ANL, pioneering exploratory measurements with long-lived, radioactive Ra isotopes will be performed.

Specifically, the ²²⁵Ra nucleus will be investigated first, in order to provide input for the EDM measure- ment currently being prepared at ANL using atom trapping technology. The focus of the GRETINA ex- periment is on the identification of the collective octu- pole band sequences that would be built on the so- called parity-doublet states; i.e., pairs of bands with the same K quantum number, but opposite parity where states of the same spin are rather close in excitation energy so that they can be described as the projections from a single intrinsic state of mixed parity.

At the FRIB reaccelerator, high-statistics multi-step Coulomb excitation with GRETA will be possible for the ²²⁵Ra and ²²³Rn nuclei; e.g, for both nuclei where efforts to measure the EDM are currently underway.

With the available beam intensities, detailed, quantita- tive studies of octupole collectivity will become possi- ble, including the precise determination of static mo- ments and transition strengths. Furthermore, new can- didate nuclei will be probed for the presence or ab- sence of octupole deformation as inferred from proper- ties of the excited levels, including spin-parity assign- ments and electromagnetic transition rates. One such possible candidate, which is out of reach for the re- quired detailed studies at present generation facilities, is ²²⁹Pa. In this nucleus, the EDM contribution induced by the Schiff moment is predicted to be 3 x 10⁴ times larger than the one for (spherical) ¹⁹⁹Hg and 40 times larger than the contribution to one of the most promis- ing candidates today, ²²⁵Ra [Fla08]. Little is known about the structure of ²²⁹Pa to date: most spin-parity assignments are uncertain and no information exists on

transition strengths or moments. At FRIB, ²²⁹Pa will be available at reaccelerated-beam rates of the order of 10⁶/s allowing for first-rate, inverse-kinematics Cou- lomb excitation measurements. In addition to the high detection efficiency, the angular coverage and tracking ability of GRETA will be invaluable to exploit linear polarization and angular distributions in the characteri- zation of possible new, game-changing EDM candidate nuclei like ²²⁹Pa and, perhaps, entirely new candidates not envisioned today.

4+ 2+ 2+0+ 6+ 4+ 2+ 2+ 2+ 0+

Miniball at ISOLDE

4+ 2+ 2+0+ 6+ 4+ 1- 0+ 2+ 2+ 3- 2+

7- 5-

GRETA at FRIB

GateGRETA at FRIB 276keV 7 5 coincidences Gate on 7^- 5^-

Figure 2.3.1 Upper panel: GEANT4 simulation repro- ducing the ²²⁰Rn ray spectrum from Coulomb excita- tion carried out using Miniball at REX-ISOLDE with a radioactive beam of ²²⁰Rn at 2.8MeV/u from [Gaf13].

Middle panel: Simulated spectrum for ²²⁰Rn Coulomb excitation carried out at FRIB using GRETA. Lower panel: Simulated spectrum of ²²⁰Rn from GRETA at FRIB gated on the 7^- -> 5^- 276 keV transition.

HRS + GRETA for the most neutron rich nuclei at FRIB

Simulated CoulEx spectrum for ²²⁰Rn at FRIB using GRETA

Superb resolving power

12  

What FRIB’s power buys you (examples)

Neutron number

Proton number

FRIB CARIB

U

New drip-line nuclei

Possible to study

FAIR - 11 cases RIBF - 13 cases FRIB - 24 cases

FRIB RIBF FAIR

22C

24O

30Ne

34Ne

37Na

40Mg

42Si

47P

50S⁵³Cl

54Ar ⁶⁰Ca ⁷⁸Fe ⁸⁴Ni⁸⁷Cu

Access to nuclei with large neutron skins

Reach into the r-process nuclei:

masses and detailed spectroscopy of the r-process path nuclei

DFT   FRIB  

current  

More discovery potential

Access to the N/Z dependence and continuum effects broadly. This will allow us to explore new paradigms of nuclear structure in the domain where many-body

correlations, rather than the nuclear mean-field, dominate.

Some Anticipated NS Greatest Science Hits: next 15+ years

•  We will understand QCD origin of nuclear forces. We will develop the predictive ab- initio description of light and medium-mass nuclei and their reactions. We will have the spectroscopic-quality density functional theory that will extrapolate in mass,

isospin, and angular momentum. We will develop the comprehensive reaction theory consistent with nuclear structure.

•  We will know if very long-lived superheavy elements exist in nature. We will understand the mechanism of clustering and other aspects of open many-body systems.

•  We will have a quantitative microscopic model of fission that will provide the missing data for nuclear security, astrophysics, and energy research. We will predict

important astrophysical reaction rates and nuclear reaction rates important for nuclear forensics and stockpile stewardship. We will have a comprehensive

description of weak transitions in nuclei and utilize them in multi-dimensional stellar evolution simulations. We will know the nuclear equation of state for normal and neutron matter from 0.1 to twice the saturation density. We will improve the

sensitivity of EDM searches in atoms by one to two orders of magnitude over current limits.

Wha t are nucl ei go od fo r?

How are nucl ei org anize d?

Whe re do nucl ei co me f rom?

Symmetry energy

Symmetry energy slope

Quest for understanding the neutron-rich matter on Earth and in the Cosmos

Data Bounds on EOS

Crustal structures

EOS with hyperons

Towards predictive capability The crucial role of HPC

16

While FRIB will explore uncharted regions of the nuclear chart and produce rare

isotopes important for astrophysics, fundamental symmetries, and applications, there is a key component of the program that links this exploration to studies of near-stable isotopes.

•  The ATLAS stable beam facility has world-unique capabilities that will enable necessary precision studies near stability and at the limits of atomic number.

•  The electron beam at JLAB provides a unique capability for probing the short- range part of the nuclear force in nuclei and the modification of nucleons in the nuclear medium.

•  The photon beams at HIγS and neutron beams at Los Alamos are unique capabilities.

•  The university accelerator labs have a special role. They contribute cutting edge science, targeted research programs of longer duration, critical developments of techniques and equipment, combined with hands-on training.

•  Tremendous scientific opportunity

•  Complementarity

•  Cost-effectiveness

Poised to make major advances

How can the knowledge and technological progress provided by nuclear physics best be used to benefit society?

•  Energy (fission, reactions, decays…)

•  Security (stewardship, forensics, detection…)

•  Isotopes (medicine, industry, defense, applied research…)

•  Industry (radiation, ion implantation…)

Nuclei Matter

Profound intersections

•  Astrophysics

•  Fundamental Symmetries

•  Complex systems

•  Computing

Our current understanding has benefited from technological improvements in

experimental equipment and accelerators that have expanded the range of available isotopes and allowed individual experiments to be performed with only a small

number of atoms. Concurrent advances in theoretical approaches and computational science have led to a more detailed understanding and pointed toward which nuclei and what phenomena to study. The prospects are exciting.

Joint Resolutions from the Low-Energy Nuclear Physics and Nuclear Astrophysics Town Meetings (see Interim Summary)

1.  The highest priority in low-energy nuclear physics and nuclear astrophysics is the timely completion of the Facility for Rare Isotope Beams and the initiation of its full science program

2.  While FRIB is the top priority of both subfields, there are other capabilities needed to reach the scientific goals. In arriving at a joint set of resolutions, the Town Meeting participants

addressed priorities for the field as a whole. What emerged is a coherent plan that pursues key scientific opportunities by leveraging existing and future facilities. The plan involves

continuation of forefront research activities, development of needed theory, and initiation of a focused set of new equipment initiatives. While many specific ideas were discussed, it was decided to approve wording that made clear that the community is asking for the base set of needs while recognizing that some initiatives may have to be delayed.

a.  We recommend appropriate support for operations and planned upgrades at ATLAS, NSCL, and university-based laboratories, as well as for the utilization of these and other facilities, for continued scientific leadership. Strong support for research groups is essential.

b.  We recommend enhanced support for theory in low-energy nuclear science and nuclear astrophysics, which is critical to realize the full scientific promise of our fields.

c.  We recommend targeted major instrumentation and accelerator investments to realize the discovery potential of our fields.

Joint Resolutions from the Low-Energy Nuclear Physics and Nuclear Astrophysics Town Meetings (2)

3.  We endorse the recommendations of the 2014 Computational Nuclear Physics Meeting: “Capitalizing on the pre-exascale systems of 2017 and beyond requires significant new investments in people, advanced software, and complementary capacity computing directed toward nuclear theory.”

4.  We endorse the recommendation of the DNP Town Meeting on Education and Innovation.

Specific Resolutions from the Low-Energy Nuclear Town Meeting

•  We recommend that enhanced support for nuclear theory be provided to address key questions in nuclear physics and astrophysics and to realize the full potential of the experimental program at FRIB. We recommend the creation of a national FRIB theory center to drive this exciting science and the computational nuclear physics initiative to take maximum advantage of high performance computing critical to this effort.

•  To realize the full scientific discovery potential of FRIB and existing facilities it is essential that major experimental systems are available. We recommend:

o  The construction of the 4π GRETA detector in a timely manner.

o  The timely construction of other new state-of-the-art instruments for FRIB, such as the High-Rigidity Spectrometer and the separator for capture

reactions SECAR.

o  The construction of ReA12 in a timely manner.

BACKUP

What has been accomplished since 2007?

•  Experimental  demonstra:on  that  the  textbook  knowledge  on  nuclear  structure  must  by   revised.  We  now  know  that  the  nuclear  shell  model  breaks  down  in  neutron-­‐rich  nuclei.  The   driving  forces  behind  the  changes  can  only  be  isolated  in  the  most  exo:c  nuclei,  providing   crucial  informa:on  on  the  interac:ons  (3N,  tensor)  that  cannot  be  gained  from  stable   nuclear  species.  

•  By  reaching  ⁴⁰Mg,  ⁵⁴Ca,  and  ²⁶O  (unbound),  and  studying  spectroscopy  of  ⁵⁴Ca  and  ⁶⁰Ti, we   put  strong  constraints  on  the  models  of  nuclear  binding.  

•  Tomography  of  2p,  2n,  and  β-­‐np  decays  and  precise  data  on  charge  radii  of  halo  nuclei   provided  unique  informa:on  on  correla:ons  between  weakly-­‐bound/unbound  nucleons.  

The  doubly-­‐magic  ⁴⁸Ni  nucleus,  ground-­‐state  2p  emi`er,  has  been  observed  for  the  first   :me.    

•  Evidence  for  state-­‐dependent  pairing  above  ¹⁰⁰Sn  and  observa:on  of  superallowed  GT  beta   decay  of  ¹⁰⁰Sn.    

•  First  measurements  with  single-­‐nucleon  transfer  reac:ons  and  Coulomb  excita:on  ini:ated   by  neutron-­‐rich  rare-­‐isotope  beams  of  :n  around  the  doubly-­‐magic  nucleus  ¹³²Sn.  Precision   mass  measurements  on  a  large  sample  of  new  neutron-­‐rich  isotopes  around  ¹³²Sn.  

•  Gamma-­‐ray  spectroscopy  of  ¹⁵⁸Er  has  revealed  collec:ve  rota:on  at  record  ultra-­‐high   angular  momentum  approaching  80  ћ.    

•  Confirma:on  of  octupole  correla:ons  in  Ra  and  Rn  nuclei  involved  in  EDM  measurements  

•  Discovery  of  elements  114-­‐118    and  confirma:on  of  existence  of  other  superheavy  nuclei.  

The  new  data  indicate  that  we  are  moving  toward  the  shores  of  the  region  of  enhanced   stability.  Spectroscopy  of  nuclei  with  Z>102.    Chemistry  of  Z=106  and  114.  

•  The  neutron  skin  was  probed  experimentally  using  new  techniques.  PREX  experiment  

demonstrated  the  feasibility  of  the  parity  viola:ng  electron  sca`ering  for  the    determina:on   of  radius  of  neutron  distribu:on.  The  electric  dipole  polarizability  was  shown  to  provide  

complementary  informa:on;  it  was  determined  precisely  in  several  heavy  nuclei.  

•  Comprehensive  evalua:on  of  GT  transi:on  strengths  for    nuclei  of  importance  for  electron-­‐

captures  in  supernovae  and  accre:ng  neutron-­‐star  crusts,  including  the  key  nucleus  ⁵⁶Ni.  

•  Extrac:on  of  the  quark-­‐mixing  matrix  element  V_ud  from  superallowed  beta-­‐decays  has   confirmed  that  unitarity  of  CKM    matrix  holds  to  an  unprecedented  precision.  

•  Lamce  QCD  descrip:on  of  nucleus-­‐nucleus  sca`ering,  light  nuclei,  and  hypernuclei.  

•  Deriva:on  and  op:miza:on  of  chiral  NN+3N  interac:ons.  

•  Nucleonic  pairs  in  nuclei  at  very  short  distances  explained  in  terms  of  tensor  correla:ons.  

•  Quan:ta:ve  ab-­‐ini:o  nuclear  structure  &  reac:on    calcula:ons  for  light  and  medium-­‐mass   nuclei,  and  nuclear  ma`er.  Those  include  the  first  descrip:on  of  the  Hoyle  state  in  ¹²C,   explana:on  of  a  useful  long  half-­‐life  of  ¹⁴C  crucial  for  carbon  da:ng,  n+t  cross  sec:on   predic:ons  for  iner:al  confinement  fusion  ;  spectroscopy  of  ⁵⁴Ca;  descrip:on  of  neutrino-­‐

nucleus  interac:ons;  and  impact  of  3N  forces  on  the  neutron  star  radius.  

•  Quan:ta:ve  DFT  descrip:on  of  heavy  nuclei,  with  uncertainty  quan:fica:on.  Those  include   predic:ons  of  driplines;  spontaneous  fission  life:mes  for  ac:nides  and  superheavy  nuclei;  

isospin  mixing  correc:ons  for  superallowed  beta  decays;  and  descrip:on  of  nuclear  and   atomic  superfluid  condensates.  

•  Development  of  nonlocal  dispersive  op:cal  model  capable  of  providing  realis:c  extrapola:ons   to  neutron  rich  systems.    

What has been accomplished since 2007? (cont)

• One-­‐body  currents    

• Two-­‐nucleon  currents  

Two-­‐Nucleon  Currents:  Moments  and  Transi:ons  

Magne:c  Moments  

Ikeda  sum  rule  (measure  for  beta-­‐decay   strength)  in  ¹⁴C  and  ^22,24O  as  a  func:on  of  a   three-­‐body-­‐force  parameter.  Gray  area  is   region  of  physical  interest,  determined  by   the  triton  half  life.  The  quenching  of  8-­‐16%  

agrees  with  measurements  in  heavier   nuclei.  

-1 -0.5 0 0.5 1

cD

0.8 0.9 1

(S −−S +) [3(N − Z)]

14C, Λ_χ = 500MeV

22O, Λ_χ = 500MeV

24O, Λ_χ = 500MeV

14C, Λ_χ = 450MeV

22O, Λ_χ = 450MeV

24O, Λ

χ = 450MeV

14C, Λ_χ = 550MeV

24O, Λ_χ = 550MeV

22O, Λ_χ = 550MeV

Quenching  of  GT  strength  

1B and 2B χEFT EM currents

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Sn region: structure and r-process

Trends indicate nuclei are less bound with neutron excess (affects the location of the r- process path

Large disagreement with results obtained with β-decay measurements

Penning trap measurements

Transfer studies

(d,p)

(⁹Be, ⁸Be)

Quantified Nuclear Landscape

DFT   FRIB  

current  

Requested targets will enable a wide-ranging international SHE research program

•  After 2020: GSI ²⁴³Am, ²⁴⁴Pu, ²⁴⁸Cm, ²⁴⁹Bk

€

λ_n ~ Δ_n

Studies of the N/Z dependence of the nuclear force and continuum effects broadly. Such investigations will allow us to explore new paradigms of nuclear structure in the domain where many-body correlations, rather than the nuclear mean-field, dominate.

The Quest: Towards long-lived superheavy nuclei

Current  0νββ  predic:ons  

J. Phys. G: Nucl. Part. Phys. 39 (2012) 124002 P Vogel

0 1 2 3 4 5 6 7 8

M0ν

76Ge ⁸²Se ⁹⁶Zr ¹⁰⁰Mo ¹³⁰Te ¹³⁶Xe ¹⁵⁰Nd

RQRPA IBM-2NSM PHFBEDF

Figure 9. Dimensionless 0νββ nuclear matrix elements for selected nuclei evaluated using a variety of indicated methods. For references see text.

The nuclear shell model (NSM) is, in principle, the method that seems to be well suited for this task. In it, the valence space consists of just few single particle states near the Fermi level (usually one main shell). With interaction that is based on the realistic nucleon–nucleon force, but renormalized slightly to describe better masses, energies and transitions in real nuclei, all possible configurations of the valence nucleons are included in the calculation. The resulting states have not only the correct number of protons and neutrons, but also all relevant quantum numbers (angular momentum, isospin, etc). For most nuclei of interest (⁴⁸Ca is an exception) the valence space, however, does not include enough states to fulfil the Ikeda sum rule (see equation (10)), hence full description of the β strength functions S^β± is not possible. However, NSM is well tested, since it is capable to describe quite well the spectroscopy of low lying states in both initial and final nuclei. In the following figures9–11the NSM results are denoted by the blue squares.

The 2νββ decay matrix elements M^2ν for several nuclei in table 1 are reasonably well described in the NSM, see [44] (¹⁰⁰Mo being a notable exception). However, to achieve this task, it was necessary to apply quenching factors that, for nuclei heavier than ⁴⁸Ca, are considerably smaller than in the lighter nuclei where the valence space contains the full oscillator shell. Note that no quenching is applied to the results shown in figures 9–11. I will describe the issue of quenching of the weak nucleon current operators in section 9.

The QRPA and its renormalized version (RQRPA) is another method often used in the evaluation of M^0ν. In it, the valence space is not restricted and contains at least two full oscillator shells, often more than that. On the other hand, only selected simple configurations of the valence nucleons are used. The basis states have broken symmetries in which particle numbers, isospin, and possibly angular momentum are not good quantum numbers but conserved only on average. After the equations of motion are solved, some of the symmetries are partially restored. The RQRPA partially restores the Pauli principle violation in the resulting states.

The procedure consist of several steps. In the first one the like particle pairing interaction is taken into account, using the BCS procedure. Then, the neutron–proton interaction is used in the equations of motion, resulting in states that contain two quasiparticle and two quasihole configurations and their iterations. Usually, the realistic G-matrix based interaction is used, but

17

“There  is  generally  significant  varia4on  among  different  calcula4ons  of  the  nuclear  matrix   elements  for  a  given  isotope.  For  considera4on  of  future  experiments  and  their  projected   sensi4vity  it  would  be  very  desirable  to  reduce  the  uncertainty  in  these  nuclear  matrix   elements.”      (Neutrinoless  Double  Beta  Decay  NSAC  Report  2014)  

Our  theore:cal  0νββ  strategy  

0.1 0.2

76Ge

0 0.1 0.2

0 2 4 6 8 10

|Y(f)|2

f = pn pairing amplitude

76Se

Ab-­‐ini&o  

Solve  “g_A–quenching  problem”  

•  Construct  shell  model  interac:ons  and  effec:ve  GT   operator  from  coupled  cluster  or  IMSRG  calcula:ons  in   sd-­‐shell  nuclei.    Include  two-­‐body  currents.  

•  Obtain  two-­‐body  effec:ve  GT  shell-­‐model  operators  for   use  with  nuclei  throughout  sd  shell.    This  will  allow  us  to   determine  how  much  of  g_A  renormaliza:on  is  due  to   two-­‐body  currents,    and  how  much  to  correla:ons   outside  the  phenomenological  shell  model.    

Apply  same  methods  to  0νββ  decay    

•  Construct  effec:ve  double-­‐beta  operators  as  well.    This   procedure  and  g_A  work  will  tell  us  whether  0νββ  decay   is  quenched  anywhere  near  as  much  as  2νββ  decay.  

•  Scale  up  to  pfg  shell,  ⁷⁶Ge,  ⁸²Se,  other  shells  for,  e.g.,  

136Xe  

Apply  other  methods  to  closed-­‐shell  isotopes,  e.g.,  

48Ca,  ²²O  

•  Benchmark  Quantum  Monte  Carlo,  coupled  cluster   theory,  and    NCSM.    

DFT  

Add  all  collec:ve  DOFs  to  GCM  

•  Include  pn  pairing,  pp  and  nn  pairing,  triaxial  

deforma:on  as  coordinates.  Preliminary  indica:ons   are  that  this  may  be  enough  for  good  0νββ  results.      

GCM  probably  best  op:on  in  heavier  systems;  can   compute  all  candidate  nuclei  plus  some  sd-­‐shell   isotopes.  

Understand  overlaps  of  ini:al  and  final  states  In   QRPA  

•  Going  beyond  quasi-­‐boson  approxima:on.  

Second  QRPA  

•  Will  give  more  accurate  descrip:on  of  low-­‐lying  GT   strength.  

All  these  methods  work  with  controlled  expansions  of  interac:ons   and  operators.    Comparing  results  in  nuclei  that  can  be  treated  with   more  than  one  method,  and  with  data,    will  help  quan:fy  error.  

Worldwide  Rare  Isotope  Facili:es  

Vibrant  field  with  two  facility  classes:  Large  scale  and  targeted.  The  large  facili:es  could  do   everything,  but  targeted  programs  yield  faster  overall  progress,  more  innova:on,  and  are  

more  economical   ³²  

Two  Major  Types  ISOL  and  In-­‐Flight  

ISOL  

•  Highest  intensi:es  for  a   limited  set  of  beams  –  

40%  of  the  periodic  table  

•  TRIUMF  ISAC/ARIEL  

•  HE  ISOLDE  at  CERN  

•  GANIL/SPIRAL2  

•  EURISOL  (Future)  

In-­‐Flight  

•  All  elements  and  half-­‐lives  

•  Experiments  at  200  MeV/u   –  luminosity  gain  of  10

•  FRIB  

•  GSI/FAIR  

•  RIKEN  –  current  leading   facility  

beam

target

beam

target

33  

Facility  Timelines  

The  start  dates  of  some  facili:es  (SPRIRAL2,  ARIEL,  FAIR,  RISP)  are  not  yet  firm   ³⁴  

Lies,  Damn  Lies,  and  RIB  Predic&ons  

P. Butler, ISOLDE workshop 2014 ³⁵  

•  FAIR is based on

synchrotrons and has 1.5 GeV/u and option for storage rings

•  High energy is an advantage for

production of high-Z nuclei

•  No reaccelerated beams

•  Synchrotron intensity is limited by space

charge effects

Head to head: FRIB Compared to FAIR

LISE++ EPAX3 "

The full r-process program of half-lives, masses, transfer to get (n,γ), fission studies, will take 5 to 10 years at FRIB. The equivalent program at FAIR will take 150 to 300 years

Head to head: FRIB Compared to RIKEN RIBF

LISE++ EPAX3 "

•  RIBF is based on cyclotrons and is operational now

•  Intensity is limited by stripping of ions between cyclotrons (3 times)

•  No reaccelerated beams

The full r-process program of half-lives, masses, transfer to get (n,γ), fission studies, will take 5 to 10 years at FRIB. The equivalent program at RIKEN will take 150 to 300 years

A targeted set of new instrumentation and accelerator investments are necessary.

FRIB will be a world-leading accelerator and will yield the best science when coupled with world-leading equipment. The community has identified and prioritized a suite of specialized detector systems and re-accelerator upgrades that will enable effective utilization of FRIB. In the 2007 LRP the major new detector proposed was GRETA and, at that time, it was recognized that an astrophysics separator would be needed (which is now named SECAR). It was thought that most other equipment could be repurposed. While this is still the plan, by the time FRIB becomes operational, it will have been 15 years since 2007, and major advances in detection and separator technology have or will have taken place. To this end, the community has developed exciting ideas for key new equipment. Not all can be realized immediately, but a

targeted suite to address the highest-priority research programs is needed.

•  To realize the full scientific discovery potential of FRIB and existing facilities it is essential that major experimental systems are available. We

recommend:

•  The construction of the 4π GRETA detector in a timely manner.

•  The timely construction of other new state-of-the-art instruments for FRIB, such as the High-Rigidity Spectrometer and the separator for capture

reactions SECAR.

•  The construction of ReA12 in a timely manner.

FRIB  TC  

SAB  

university national lab

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