“China-Japan Collaboration Workshop on Nuclear Mass and Life
for Unravelling Mysteries of r-process”
June 26th – 28th, 2017, Tsukuba, Japan

Beyond mean-field description ofGamow-Teller resonance and βdecay half-lives
Yifei Niu
牛一斐Collaborators: C. L. Bai, G. Colo, J. Meng, Z. M. Niu, H. Sagawa, E. Vigezzi

Gamow-Teller Resonance and β decay• Gamow-Teller Resonance
Wakasa, et al., PRC 85, 064606 (2012)

Gamow-Teller transition

ΔS=1 ΔL=0 ΔT=1
operator

Transition probabilityStrong• β-decay dominated by low-energy GT transition

Transition strength S= smoothed Bweak2

How Were the Heavy Elements Made?
The 11 greatest unanswered questions of physics
Question 3
How were the heavy elementsfrom iron to uranium made?
rapid neutron capture process(r-process)nuclear physics inputs:
mass, β-decay half-lives, …
setting the time-scale of r-process3Experimental Investigations
Proton Number

50

1E+02
5E+01
1E+01
5E+00
1E+00
5E-01
1E-01
5E-02
1E-02

r-path
28

28

50

82

Neutron Number• Development of radioactive ion-beam facilities => important advances• 78Ni and around Hosmer, et al., PRL 94, 112501, 2005; Xu, et al., PRL 113, 032505, 2014• very neutron rich Kr to Tc isotopes Nishimura, et al., PRL 106, 052502, 2011
• Zn Ga isotopes Madurga et al., PRL 109, 112501, 2012
• 110 neutron-rich nuclei across N=82 shell gap Lorusso, et al., PRL 114, 192501,2015• 94 neutron-rich nuclei from Z=55-67 Wu, et al., PRL 118, 072701, 2017
• provide a good test ground for theoretical models
4Lifetime Is a Hard Problem …
• RHB+QRPA• Skyrme HFB+QRPA

78Ni
78Ni.
Niksic, et al., PRC 71, 014308 (2005)

Engel, et al., PRC 60, 014302 (1999)• Half-lives are overestimated• Due to the nuclear structure part – Gamow-Teller transition5

Density Functional Theory• Nucleus: quantum many-body system• Density Functional Theory (DFT)E = Ψ Ĥ Ψ = Φ Ĥ eff Φ = E[ρ̂ ]Φ Slater determinant ⇔ ρ̂ 1-body density matrix

many-body problem
one-body problem
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Skyrme Density Functional• Effective HamiltonianĤef f = T̂ + V̂ef f• Skyrme Effective Interaction• Around 11 parameters to fit the nuclear observables: ti, xi, W0, α (SkM*, SLy5, …)• Successful to describe almost the whole nuclear chart: g.s. and excited states
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Random Phase Approximation (RPA)• RPA: widely used model for the description of collective vibration
ü Small oscillation: linear limit of time dependent DFT theory
keep the linear termHarmonic oscillation

ü Solution on basis
The RPA excited state (collective vibration state) is generated by• RPA: magic nuclei• Quasiparticle RPA (QRPA): superfluid nuclei
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Limits of (Q)RPA Description• (Q)RPA cannot describe thespreading width• Correlations beyond RPARPA

B
1p1h• Spreading Width (Damping Width)energy and angular momentum ofcoherent vibrations→ more complicated states of 2p2h, 3p-3h, … character

BE

1p1h
2p2h
E
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Solution: RPA + PVC

RPA•Second RPA drozdz et al., PR 197, 1 (1990)
Gambacurta et al., PRC 81, 054312 (2010)•RPA + PVC (particle vibration coupling)

Low-lying vibration
phonons |N>•RPA+PVC model based on Skyrme DFT•

Colo et al., PRC 50, 1496 (1994); Niu et al., PRC 85, 034314 (2012)
RPA+PVC model based on relativistic DFT Litvinova et al., PRC 75,064308 (2007)10

RPA+PVC: Gamow-Teller Resonance• Improved description of GT resonance in 208Pb
Y. F. Niu, G. Colo, and E. Vigezzi, Phys. Rev. C 90, 054328 (2014)

ΔS=1 ΔL=0

ü Develop a spreading widthüReproduce resonance lineshape11

RPA+PVC: β-Decay Half-Lives• Improved description of β-decay half-lives

ü Reduce half-lives systematicallyü Reproduce β-decay half-lives

Y.F. Niu, Z. M. Niu, G. Colo, and E. Vigezzi, Phys. Rev. Lett. 114, 142501 (2015).

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How PVC reduces half-lives?

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How PVC reduces half-lives?

14RPA+PVC: only for magic nuclei…

Taken from Nature News & Views 465 2010

ØTo include pairing correlations for superfluid nuclei
Quasiparticle RPA + quasiparticle vibration coupling(QRPA)+ (QPVC)ü for the study of Gamow-Teller resonance in superfluid nuclei
ü for the study of β-decay half-lives of the whole isotopic chain
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QRPA+QPVC model
Step 1: HFB+QRPA calculation (charge-exchange)=> Gamow-Teller response in QRPA level
HFB+QRPA calculation (non-charge-exchange) => vibrational phonons 1-, 2+, 3-, 4+, 5Particle-particle interaction

The QRPA equation will give the energy, and wavefunction

Step 2: QPVC calculation => Gamow-Teller response in QRPA+QPVC level
The QRPA+QPVC equation reads

where, and the

The GT strength function

matrices contain the spreading contributions, e.g.,16Spreading Terms
The matrix elements of the spreading term in the quasiparticle basis

whererepresents a doorway state, and a, b are quasi-particle states.
The vertex reduced matrix element:17

Isoscalar Pairing
Particle-particle interaction

f = 0 : without isoscalar pairing
f = 1 : with isoscalar pairing
Effect of isoscalar pairing• QRPA level• Increase the low-lying strength• Decrease the splitting between two
high-lying states• QRPA+QPVC level• Increase the low-lying strength• Similar profile
Niu, Colo, Vigezzi, Bai, Sagawa, PRC
94, 064328 (2016)18

GT Strength Distribution• (3He,t) data: cross section ✕ 1.6 so that the main GTR strength exhausts 65% sum rulePham, et al., PRC 51, 526 (1995)
overestimate the low-lying strength• (p,n) data: normalized by unit cross section
Sasano, et al., PRC 79, 024602 (2009)ü QRPA + QPVC• Develop a width of 5.3 MeV (6.4 MeV from exp.), reproduce exp. profile in GTR• Overestimate the low-lying strength
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Cumulative Sum
Cumulative sum

Cumulative sum with normalized data

• f=0 -> f=1
ü low-lying strength is increased for both QRPA and QRPA + QPVC• QRPA -> QRPA+QPVC:ü better reproduces the exp. profile
ü cumulative strength is quenched by 10% at E=25 MeVü QRPA+QPVC strength ✕ 0.75 = exp. strength ((p,n) data) at E=25 MeV
Niu, Colo, Vigezzi, Bai, Sagawa, PRC 94, 064328 (2016)20

β-Decay Half-Lives in Ni isotopes• Isoscalar Pairing:
not so effective for Ni isotopes(nuclei before N=50 closed shell)• QPVC:
reduce the half-lives
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β-Decay Half-Lives in Sn isotopes• Isoscalar Pairing:effective for Sn isotopes(nuclei above N=82 closed shell)• Isoscalar Pairing + QPVC:
reduce the half-lives
22Summary and Perspectives
Summary• Gamow-Teller transition is an important spin-isospin mode ofnucleus; β-decay is mainly determined by low-energy GTtransition• Going beyond RPA: RPA+PVC
ü Spreading widthü Reduce the half-lives• Going beyond QRPA + pairing correlations: QRPA+QPVC
ü Effect of QPVCü Effect of isoscalar pairingPerspectives• Deformation Effect• Forbidden transitions
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Thank you!
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