The relativistic and nonrelativistic finite temperature proton-neutron quasiparticle random phase approximation (FT-PNQRPA) methods are developed to study the interplay of the pairing and temperature effects on the Gamow-Teller excitations in open-shell nuclei, as well as to explore the model dependence of the results by using two rather different frameworks for effective nuclear interactions. The Skyrme-type functional SkM* is employed in the nonrelativistic framework, while the density-dependent meson-exchange interaction DD-ME2 is implemented in the relativistic approach. Both the isoscalar and isovector pairing interactions are taken into account within the FT-PNQRPA. Model calculations show that below the critical temperatures the Gamow-Teller excitations display a sensitivity to both the finite temperature and pairing effects, and this demonstrates the necessity for implementing both in the theoretical framework. The established FT-PNQRPA opens perspectives for the future complete and consistent description of astrophysically relevant weak interaction processes in nuclei at finite temperature such as $β$-decays, electron capture, and neutrino-nucleus reactions.
It is widely accepted that nuclear Gamow-Teller transitions are quenched; shell-model calculations also showed a clear anticorrelation between the Gamow-Teller strength and the transition rate of the collective quadrupole excitation from the ground state. We discuss the physics beyond this observation. It is based on the existence of spin-orbit coupling that is responsible for the non-zero probabilities of Gamow-Teller transitions in self-conjugate nuclei (N = Z). The shell-model calculations in the f p-space demonstrate the effects of the gradual artificial removal of the spin-orbit coupling …
The issue of Gamow-Teller sum rule in atomic nuclei is reexamined in the framework of a relativistic description of nuclei. It is shown that the total Gamow-Teller strength in the nucleon sector is reduced by about 12% as compared to the prediction of a non-relativistic description. This reduction is due to the antinucleon degrees of freedom.
The double Gamow-Teller strength distributions in the lightest double beta-decay candidate $^{48}$Ca and its isotope $^{46}$Ca were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of parent nucleus. The nuclear matrix element of the double Gamow-Teller transition from the ground state to the ground state that goes into the double beta decay calculation was shown as a small fraction of the total transition.
The double Gamow-Teller strength distributions in even-$A$ Calcium isotopes were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of the parent nucleus. The number of intermediate states actually contributing to the results was determined. The sum rules for the double Gamow-Teller operator in the full calculation were approximately fulfilled. In the case that the symmetry is restored approximately by introducing degeneracies of the $f$-levels, and the $p$-levels in the $fp$-model space, the agreement with the sum r…
We investigate reliability of Gamow-Teller transition strengths computed in the proton-neutron random phase approximation, comparing with exact results from diagonalization in full $0\hbarω$ shell-model spaces. By allowing the Hartree-Fock state to be deformed, we obtain good results for a wide variety of nuclides, even though we do not project onto good angular momentum. We suggest that deformation is as important or more so than pairing for Gamow-Teller transitions.
An isospin-selfconsistent pn-continuum-QRPA approach is formulated and applied to describe the Gamow-Teller strength distributions for $ββ$-decaying open-shell nuclei. The calculation results obtained for the pairs of nuclei $^{76}$Ge-Se, $^{100}$Mo-Ru, $^{116}$Cd-Sn, and $^{130}$Te-Xe are compared with available experimental data.
At forward angles, and bombarding energies E > 200 MeV, the (p,n) and (n,p) reactions are thought to be directly proportional to the Gamow-Teller transition strengths in the nuclei. Assuming that this relationship also holds for charge exchange induced by high-energy heavy ions, it would be very useful in studies with radioactive beams. Contrary to this expectation, we show that the determination of Gamow-Teller and Fermi matrix elements from heavy-ion charge-exchange at forward angles is very inaccurate.
The basic version of the semi-microscopic particle-hole dispersive optical model is implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}Ca$, $^{90}Zr$, $^{132}Sn$, and $^{208}Pb$ are compared with available experimental data.
Recently it has been shown that pseudospin symmetry has its origins in a relativistic symmetry of the Dirac Hamiltonian. Using this symmetry we relate single - nucleon relativistic magnetic moments of states in a pseudospin doublet to the relativistic magnetic dipole transitions between the states in the doublet, and we relate single - nucleon relativistic Gamow - Teller transitions within states in the doublet. We apply these relationships to the Gamow - Teller transitions from $^{39}Ca$ to its mirror nucleus $^{39}K$.
We investigate the Gamow-Teller strength distributions in the electron-capture direction in nuclei having mass A=90-97, assuming a 88Sr core and using a realistic interaction that reasonably reproduces nuclear spectroscopy for a wide range of nuclei in the region as well as experimental data on Gamow-Teller strength distributions. We discuss the systematics of the distributions and their centroids. We also predict the strength distributions for several nuclei involving stable isotopes that should be experimentally accessible for one-particle exchange reactions in the near future.
The branching ratios for E1 transitions between the spin-dipole (SD) and Gamow-Teller (GT) giant resonances in $^{90}$Nb and $^{208}$Pb are evaluated. Assuming the main GT-state has the wave function close to that for the "ideal" GT-state, we reduced the problem to calculate the SD and GT strength functions. These strength functions are evaluated within an extended continuum-RPA approach.
Starting from a Skyrme interaction with tensor terms, the $β$-decay rates of $^{52}$Ca have been studied within a microscopic model including the $2p-2h$ configuration effects. We observe a redistribution of the strength of Gamow-Teller transitions due to the $2p-2h$ fragmentation. Taking into account this effect results in a satisfactory description of the neutron emission probability of the $β$-decay in $^{52}$Ca.
We study Gamow-Teller strength distributions in some selected nuclei of particular Astrophysical interest within the iron mass region. The theoretical framework is based on a proton-neutron Quasiparticle Random Phase Approximation built on a deformed selfconsistent mean field basis obtained from two-body density-dependent Skyrme forces. We compare our results to available experimental information obtained from (n,p) and (p,n) charge exchange reactions.
We study Gamow-Teller strength distributions of 76Ge and 76Se within a deformed QRPA formalism, which includes residual spin-isospin forces in the particle-hole and particle-particle channels. We consider two different methods to construct the quasiparticle basis, a selfconsistent approach based on a deformed Hartree-Fock calculation with density-dependent Skyrme forces and a more phenomenological approach based on a deformed Woods-Saxon potential. Both methods contain pairing correlations in the BCS approach. We discuss the sensitivity of Gamow-Teller strength distributions to the deformed me…
A theoretical approach based on a deformed quasiparticle random phase approximation built on a Skyrme selfconsistent mean field is used to describe the recent measurements of the Gamow-Teller GT- strength distribution extracted from the charge-exchange reaction 76Ge(3He,t)76As with high energy resolution. The same analysis is made to describe the Gamow-Teller GT+ strength distribution measured in the 76Se(d,2He)76As reaction. Combining these two branches, the nuclear matrix element for the two-neutrino double-beta decay process is evaluated and compared to experiment. The role of the nuclear d…
We report on the calculation of Gamow-Teller and double-beta decay properties for nuclei around 132Sn within the framework of the realistic shell model. The effective shell-model Hamiltonian and Gamow-Teller transition operator are derived by way of many-body perturbation theory, without resorting to empirical effective quenching factor for the Gamow-Teller operator. The results are then compared with the available experimental data, in order to establish the reliability of our approach. This is a mandatory step, before we apply the same methodology, in forthcoming studies, to the calculation …
A version of the pn-continuum-QRPA is outlined and applied to describe the Gamow-Teller strength distributions for $ββ$-decaying open-shell nuclei. The calculation results obtained for the pairs of nuclei $^{116}$Cd-Sn and $^{130}$Te-Xe are compared with available experimental data.
We study Gamow-Teller strength distributions in the neutron-deficient even isotopes (184-194)Pb in a search for signatures of deformation. The microscopic formalism used is based on a deformed quasiparticle random phase approximation (QRPA) approach, which involves a self-consistent quasiparticle deformed Skyrme Hartree-Fock (HF) basis and residual spin-isospin forces in both the particle-hole and particle-particle channels. By analyzing the sensitivity of the Gamow-Teller strength distributions to the various ingredients in the formalism, we conclude that the beta-decay of these isotopes coul…
An isospin-selfconsistent approach based on the Continuum-Random-Phase-Approximation (CRPA) is applied to describe the Fermi and Gamow-Teller strength distributions within a wide excitation-energy interval. To take into account nucleon pairing in open-shell nuclei, we formulate an isospin-selfconsistent version of the proton-neutron-quasiparticle-CRPA (pn-QCRPA) approach by incorporating the BCS model into the CRPA method. The isospin and configurational splittings of the Gamow-Teller giant resonance are analyzed in single-open-shell nuclei. The calculation results obtained for $^{208}$Bi, $^{…
An approach for describing the hindrance of the nuclear 2νββ-decay amplitude is proposed. The approach is based on a new formula obtained by a model-independent transformation of the initial expression for the amplitude. This formula takes explicitly into account the hindrance of the decay-amplitude due to the presence of the collective Gamow-Teller state. Calculations are performed within the simplest version of the approach. Calculated and experimental 2νββhalve-lives are compared for a wide range of nuclei.
The Landau-Migdal parameter and quenching factor from the analysis of the Gamow-Teller strength distributions in medium-heavy-mass doubly-closed-shell parent nuclei
A.V. Shubnikov Institute of Crystallography of the Kurchatov Complex Crystallography and Photonics of the NRC "Kurchatov Institute", Moscow, Russia（库尔恰托夫研究所国家研究中心库尔恰托夫复合体晶体学与光子学 A.V.舒布尼科夫晶体学研究所）；National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia（莫斯科工程物理国立研究核大学）
The most precise value of V_{ud}, which is obtained from superallowed nuclear beta decay, leads to a violation of CKM unitarity by 2.2 sigma. Experiments are underway on two continents to test and improve this result through decay studies of odd-odd N = Z nuclei with A >or= 62. We show, in a series of illustrative shell-model calculations, that numerous weak Gamow-Teller branches are expected to compete with the superallowed branch in each of these nuclei. Though the total Gamow-Teller strength is significant, many of the individual branches will be unobservably weak. Thus, new techniques must…
We use the shell model Monte Carlo method to calculate complete 0f1p-shell response functions for Gamow-Teller (GT) operators and obtain the corresponding strength distributions using a Maximum Entropy technique. The approach is validated against direct diagonalization for 48Ti. Calculated GT strength distributions agree well with data from (n,p) and (p,n) reactions for nuclei with A=48-64. We also calculate the temperature evolution of the GT+ distributions for representative nuclei and find that the GT+ distributions broaden and the centroids shift to lower energies with increasing temperatu…
The scope of the paper is to apply a state-of-the-art beyond mean-field model to the description of the Gamow-Teller response in atomic nuclei. This topic recently attracted considerable renewed interest, due, in particular, to the possibility of performing experiments in unstable nuclei. We study the cases of $^{48}$Ca, $^{78}$Ni, $^{132}$Sn and $^{208}$Pb. Our model is based on a fully self-consistent Skyrme Hartree-Fock plus random phase approximation. The same Skyrme interaction is used to calculate the coupling between particles and vibrations, which leads to the mixing of the Gamow-Telle…
We study the sum rules of double Gamow-Teller (DGT) excitations through double spin-isospin operator $(σt_-)^2$. In general, $2^+$ states in the granddaughter nuclei have dominant transition strength in DGT excitations and $0^+$ states are weak, except in $T=1$ mother nuclei in which $0^+$ strength is competitive with 2$^+$ strength. The isospin selection of DGT is also discussed among 5 possible isospin states in granddaughter nuclei. A possibility to extract the unit cross section for the DGT transition strength is pointed out in the $(σt_-)^2$ excitation of double isobaric analog state (DIA…
Gamow-Teller(GT) transitions in the $β$ decays of $^9$Li and $^{11}$Li are investigated with theoretical calculations of antisymmetrized molecular dynamics. The calculated $B(GT)$ values are small for transitions to low-lying states in Be isotopes, while relatively large $B(GT)$ values are found for excited states at excitation energy $E_x\ge 10$ MeV. Sum of the $B(GT)$ values are discussed for each spin parity of final states. The calculated results seem to be inconsistent with the experimental report of the strongest GT-transition from $^9$Li to the $5/2^-$ state at 11.8 MeV of $^9$Be.
The two Gamow-Teller (GT) branches connecting the double-beta decay partners (116Cd, 116Sn) and (150Nd, 150Sm) with the intermediate nuclei 116In and 150Pm are studied within a microscopic approach based on a deformed proton-neutron quasiparticle random-phase approximation built on a Skyrme selfconsistent mean field with pairing correlations and spin-isospin residual forces. The results are compared with the experimental GT strength distributions extracted from charge-exchange reactions. Combining the two branches, the nuclear matrix elements for the two-neutrino double-beta decay are evaluate…
The energy distributions of the Gamow-Teller strength are studied for even-even Xe isotopes with mass numbers from 124 to 142. A self-consistent microscopic formalism is used to generate the single particle basis, using a deformed Skyrme Hartree-Fock mean field with pairing correlations in BCS approximation. The Gamow-Teller transitions are obtained within a quasiparticle random phase approximation (QRPA) approach using a residual spin-isospin interaction in the particle-hole and particle-particle channels. We then discuss the pairing BCS treatment and the determination of the ph and pp residu…
We investigate the effects of the spin-isospin channel of the Skyrme energy functional on predictions for Gamow-Teller distributions and superdeformed rotational bands. We use the generalized Skyrme interaction SkO' to describe even-even ground states and then analyze the effects of time-odd spin-isospin couplings, first term by term and then together via linear regression. Some terms affect the strength and energy of the Gamow-Teller resonance in finite nuclei without altering the Landau parameter g_0' that to leading order determines spin-isospin properties of nuclear matter. Though the exis…
Gamow-Teller transitions in isotopes of chromium play a consequential role in the presupernova evolution of massive stars. $β$-decay and electron capture rates on chromium isotopes significantly affect the time rate of change of lepton fraction ($\dot{Y_{e}}$). Fine-tuning of this parameter is one of the key for simulating a successful supernova explosion. The (anti)neutrinos produced as a result of electron capture and $β$-decay are transparent to stellar matter during presupernova phases. They carry away energy and this result in cooling the stellar core. In this paper we present the calcula…
We have reported a systematic shell model description of the experimental Gamow-Teller transition strength for $^{44}$Sc $\rightarrow$ $^{44}$Ca, $^{45}$Ti $\rightarrow$ $^{45}$Sc, $^{48}$Ti $\rightarrow$ $^{48}$V, $^{66}$Co $\rightarrow$ $^{66}$Ni, and $^{66}$Fe $\rightarrow$ $^{66}$Co transitions using KB3G and GXPF1A interactions for $fp$ model space. In order to see the importance of higher orbital for $^{66}$Co $\rightarrow$ $^{66}$Ni and $^{66}$Fe $\rightarrow$ $^{66}$Co transitions, we have reported the shell model results with $fpg_{9/2}$ space using GXPF1Br+$V_{MU}$ interaction. We ha…
Gamow-Teller(GT) resonances in finite nuclei are studied in a fully consistent relativistic random phase approximation (RPA) framework. A relativistic form of the Landau-Migdal contact interaction in the spin-isospin channel is adopted. This choice ensures that the GT excitation energy in nuclear matter is correctly reproduced in the non-relativistic limit. The GT response functions of doubly magic nuclei $^{48}$Ca, $^{90}$Zr and $^{208}$Pb are calculated using the parameter set NL3 and $g_0'$=0.6 . It is found that effects related to Dirac sea states account for a reduction of 6-7 % in the GT…
Role of the Landau-Migdal parameters with the pseudovector ($g_a$) and the tensor coupling ($g_t$) is examined for the giant Gamow-Teller (GT) states in the relativistic random phase approximation (RPA). The excitation energy is dominated by both $g_a$ and $g_t$ in a similar way, while the GT strength is independent of $g_a$ and $g_t$ in the RPA of the nucleon space, and is quenched, compared with that in non-relativistic one. The coupling of the particle-hole states with nucleon-antinucleon states is expected to quench the GT strength further through $g_a$.
The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF+RPA) model. The Gamow-Teller (GT) strength function of 90Zr and 208Pb are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcom…
We propose a new model to calculate stellar electron capture rates for neutron-rich nuclei. These nuclei are encountered in the core-collapse of a massive star. Using the Shell Model Monte Carlo approach, we first calculate the finite temperature occupation numbers in the parent nucleus. We then use these occupation numbers as a starting point for calculations using the random phase approximation. Using the RPA approach, we calculate electron capture rates including both allowed and forbidden transitions. Such a hybrid model is particularly useful for nuclei with proton numbers Z<40 and neutro…
Electron capture and beta-decay rates on nuclei in the mass range A=45-65 play an important role in many astrophysical environments. The determination of these rates by large-scale shell model calculations is desirable, but it requires to reproduce the Gamow-Teller strength distributions and spectra of the pf shell nuclei. We show in this paper that large-scale shell model calculations, employing a slightly monopole-corrected version of the wellknown KB3 interaction, fulfill these necessary requirements. In particular, our calculations reproduce the experimentally available GT+ and GT- strengt…
The Gamow-Teller strength in nuclei can be strongly affected by the internal degrees of freedom of the nucleon. It is demonstrated that this feature is unique to the Gamow-Teller. Excitation modes that involve spatial degrees of freedom are much less influenced by the internal excitation of nucleons. The fact that the observed Gamow-Teller strength is quenched by 30-40 percent in all nuclei suggests that indeed this is due to the nucleon excitation in nuclei.
The Gamow-Teller(GT) states are investigated in relativistic models. The Landau-Migdal(LM) parameter is introduced in the Lagrangian as a contact term with the pseudo-vector coupling. In the relativistic model the total GT strength in the nucleon space is quenched by about 12% in nuclear matter and by about 6% in finite nuclei, compared with the one of the Ikeda-Fujii-Fujita sum rule. The quenched amount is taken by nucleon-antinucleon excitations in the time-like region. Because of the quenching, the relativistic model requires a larger value of the LM parameter than non-relativistic models i…
We perform calculations for M1 transitions and allowed Gamow Teller (GT) transitions in the even-even Titanium isotopes - $^{44}$Ti, $^{46}$Ti, and $^{48}$Ti. We first do calculations with the FPD6 interaction. Then to study the effect of T=0 matrix elements on the M1 and GT rates we introduce a second interaction in which all the T=0 matrix elements are set equal to zero and a third in which all the T=0 matrix elements are set to a constant. For the latter two interactions the T=1 matrix elements are the same as for FPD6. We are thus able to study the effects of the fluctuating T=0 matrix ele…
$β$-decay half-lives of neutron-rich nuclei around $N=82$ are key data to understand the $r$-process nucleosynthesis. We performed large-scale shell-model calculations in this region using a newly constructed shell-model Hamiltonian, and successfully described the low-lying spectra and half-lives of neutron-rich $N=82$ and $N=81$ isotones with $Z=42-49$ in a unified way. We found that their Gamow-Teller strength distributions have a peak in the low-excitation energies, which significantly contributes to the half-lives. This peak, dominated by $ν0g_{7/2} \to π0g_{9/2}$ transitions, is enhanced …
We investigated effects of neutron-proton ($np$) pairing correlations comprising isoscalar (IS) and isovector (IV) component on Gamow-Teller (GT) transitions of $^{56, 58,62,64}$Ni by taking into account nuclear deformation in a deformed Woods-Saxon mean field. Our GT calculations based on a deformed Bardeen-Cooper-Schriffer (DBCS) approach have been performed within a deformed quasi-particle random phase approximation (DQRPA) which explicitly includes the deformation as well as all kinds of pairing correlations not only at the DBCS but also at the DQRPA stage. Competition of these two effects…
We propose a self-consistent quasi-particle random phase approximation (QRPA) plus quasi-particle-vibration coupling (QPVC) model with Skyrme interactions to describe the width and the line shape of giant resonances in open-shell nuclei, in which the effect of superfluidity should be taken into account in both the ground state and the excited states. We apply the new model to the Gamow-Teller resonance in the superfluid nucleus $^{120}$Sn, including both the isoscalar spin-triplet and the isovector spin-singlet pairing interactions. The strength distribution in $^{120}$Sn is well reproduced an…
Beta-decay properties of neutron-rich Zr and Mo isotopes are investigated within a microscopic theoretical approach based on the proton-neutron quasiparticle random-phase approximation. The underlying mean field is described self-consistently from deformed Skyrme Hartree-Fock calculations with pairing correlations. Residual separable particle-hole and particle-particle forces are also included in the formalism. The structural evolution in these isotopic chains including both even and odd isotopes is analyzed in terms of the equilibrium deformed shapes. Gamow-Teller strength distributions, beta…
Although many random-phase approximation (RPA) calculations of the Gamow-Teller (GT) response exist, this is not the case for calculations going beyond the mean-field approximation. We apply a consistent model that includes the coupling of the GT resonance to low-lying vibrations, to nuclei of the $fp$ shell. Among other motivations, our goal is to see if the particle-vibration coupling can redistribute the low-lying GT$^+$ strength that is relevant for electron-capture processes in core-collapse supernova. We conclude that the lowering and fragmentation of that strength are consistent with th…
In a single j-shell calculation we consider the effects of several different interactions on the values of Gamow-Teller (B(GT)'s) and magnetic moments. The interactions used are MBZE, J=0 pairing, J_{max} pairing and half and half.
We study $β$ decays within an effective theory that treats nuclei as a spherical collective core with an even number of neutrons and protons that can couple to an additional neutron and/or proton. First we explore Gamow-Teller $β$ decays of parent odd-odd nuclei into low-lying ground-, one-, and two-phonon states of the daughter even-even system. The low-energy constants of the effective theory are adjusted to data on $β$ decays to ground states or Gamow-Teller strengths. The corresponding theoretical uncertainty is estimated based on the power counting of the effective theory. For a variety o…
Gamow-Teller (GT) states in N=Z nuclei with the mass number A from 48 to 64 are studied by using Hartree-Fock-Bogoliubov + quasi-particle random phase approximation (HFB+QRPA) with Skyrme interactions. The isoscalar spin-triplet (T=0,S=1) pairing interaction is taken into account in QRPA calculations. It is found in the context of SU(4) symmetry in the spin-isospin space that the GT strength of lower energy excitations is largely enhanced by the T=0 pairing interaction which works cooperatively with the T=1 pairing interaction in the ground state. A two-peaked structure observed recently in $(…
Two-particle two-hole (2p2h) effect on the Gamow-Teller (GT) transition for neutron-rich nuclei is studied by the second Tamm-Dancoff approximation (STDA) with the Skyrme interaction. Unstable $^{24}$O and $^{34}$Si, and stable $^{48}$Ca nuclei are chosen to study the quenching and fragmentation of the GT strengths. Correlation of the 2p2h configurations causes $20$\% quenching and downward shift of GT giant resonances (GTGRs). The residual interaction changing relative angular momentum, appeared in the tensor force part, gives a meaningful effect to the GT strength distributions. In this work…
Motivated by the proposed experiment $^{14}N(d,{^2He})^{14}C$, we study the final states which can be reached via the allowed Gamow-Teller mechanism. Much emphasis has been given in the past to the fact that the transition matrix element from the $J^π=1^+ T=0$ ground state of $^{14}N$ to the $J^π=0^+ T=1$ ground state of $^{14}C$ is very close to zero, despite the fact that all the quantum numbers are right for an allowed transition. We discuss this problem, but, in particular, focus on the excitations to final states with angular momenta $1^+$ and $2^+$. We note that the summed strength to th…
Gamow-Teller (GT) and spin-dipole (SD) strength distributions of four doubly magic nuclei $^{48}$Ca, $^{90}$Zr, $^{132}$Sn and $^{208}$Pb are studied by the self-consistent Hartree-Fock plus random phase approximation (RPA) method. The Skyrme forces SAMi and SAMi-T without/with tensor interactions are adopted in our calculations. The calculated strengths are compared with available experimental data. The RPA results of GT and SD strengths of all four nuclei show fine agreement with observed GT and SD resonances in energy. A small GT peak below the main GT resonance is better described by the S…
