Gamow-Teller Operator Research Articles

The renormalization of the shell-model Gamow-Teller operator starting from effective field theory for nuclear systems

The renormalization of the shell-model Gamow-Teller operator starting from effective field theory for nuclear systems

Neutrinoless double beta decay theory

Within left-right symmetric model a generalization of the Majorana neutrino mass for the case of light and and heavy neutrinos is introduced and analyzed. Further, current status of calculation of the neutrinoless double beta decay matrix elements is shortly reviewed. An important connection between them and matrix element of double Gamow-Teller operator is established. A new way of fixing quenching of axial-vector coupling constant gA is presented.

Renormalization of the Gamow-Teller operator within the realistic shell model

In nuclear structure calculations, the choice of a limited model space, due to computational needs, leads to the necessity to renormalize the Hamiltonian as well as any transition operator. Here, we present a study of the renormalization procedure and effects of the Gamow-Teller operator within the framework of the realistic shell model. Our effective shell-model operators are obtained, starting from a realistic nucleon-nucleon potential, by way of the many-body perturbation theory in order to take into account the degrees of freedom that are not explicitly included in the chosen model space. The theoretical effective shell-model Hamiltonian and transition operators are then employed in shell-model calculations, whose results are compared with data of Gamow-Teller transition strengths and double-beta half-lives for nuclei which are currently of interest for the detection of the neutrinoless double-beta decay process, in a mass interval ranging from A=48 up to A=136. We show that effective operators are able to reproduce quantitatively the spectroscopic and decay properties without resorting to an empirical quenching neither of the axial coupling constant gA, nor of the spin and orbital gyromagnetic factors. This should assess the reliability of applying present theoretical tools to this problematic.

Nuclear structure studies of double-charge-exchange Gamow-Teller strength

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 rules was very close.

Nuclear axial currents from scale-chiral effective field theory**Supported by National Science Foundation of China (NSFC) (11475071, 11547308) and the Seeds Funding of Jilin University

By incorporating hidden scale symmetry and hidden local symmetry in the nuclear effective field theory, combined with the double soft-pion theorem, we predict that the Gamow-Teller operator coming from the space component of the axial current should remain unaffected by the QCD vacuum change caused by the baryonic density, whereas the first forbidden beta transition operator coming from the time component should be strongly enhanced. While the latter has been confirmed for some time, the former was given support by a powerful recent ab initio quantum Monte Carlo calculation for light nuclei, which also confirmed the old “chiral filter hypothesis.” Formulated in terms of the Fermi-liquid fixed point structure of strong-coupled nuclear interactions, we offer an extremely simple resolution to the long-standing puzzle of the “quenched gA,” [], found in nuclear Gamow-Teller beta transitions, giant Gamow-Teller resonances, and double beta decays.

Study of the double Gamow-Teller transitions using the shell model approach

The double Gamow-Teller strength distributions in the lightest double beta-decay candidate 48Ca and its isotope 46Ca 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.

Nuclear structure features of Gamow-Teller excitations

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 that influences Gamow-Teller and quadrupole modes in opposite way. The realistic spin-orbit splitting moves the cumulative Gamow-Teller strength up and leads to stronger fragmentation; both trends are discussed in terms of simple symmetry arguments. Along with this process, the Gamow-Teller operator excites, in addition to the main line of L = 0 states, states with L = 2 which should be added, with the interference terms, to account for the total strength.

Calculation of Gamow-Teller and two-neutrino double- β decay properties for Te130 and Xe136 with a realistic nucleon-nucleon potential

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 of the neutrinoless double-beta decay nuclear matrix element for nuclei that are currently considered among the best candidates for the detection of this process.

The Dependence of Gamow-Teller and Isobaric Analogue Resonances on The Mean Field Parameters

The variation of Gamow-Teller and isobaric analogue resonances by the mean field parameters for double magic nuclei such as and has been searched within the framework of quasi random phase approximation (QRPA). The nucleon-nucleon effective interaction potential has been defined by considering the commutativity of the Gamow-Teller operator with the central term in the nuclear part of the total Hamiltonian. The effective interaction constant has been found from this commutativity and taken out to be a free parameter.

Gamow-Teller Strength Distributions for Some Magic Nuclei

The total Gamow-Teller strengths and their energy distributions for 96Zr, 96Sr, 54Ca, 28O, 24C and 14C have been obtained within the framework of Random Phase Approximation (RPA). The effective interaction potential has been described by considering the commutativity of the Gamow-Teller operator with the central part of the nuclear Hamiltonian.

The investigation of the 2νββ decay by Pyatov method within quasiparticle random phase approximation formalism

The violated commutation condition between the total shell model Hamiltonian and Gamow-Teller operator (GT) has been restored by Pyatov method (PM). The considered nuclear model Hamiltonian in PM includes the separable GT residual interaction in ph and pp channels and is differentiated from the traditional schematic model by h 0(restoration term). The influence of the h 0 effective interaction on the 2νββ decay of 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128,130Te and 136Xe is investigated. All the calculations have been done within the framework of standard QRPA. The results obtained by PM are compared with those of other approaches and experimental data. The influence of the restoration term on the stability of the 2νββ decay nuclear matrix elements is analysed.

Piecewise moments method: Generalized Lanczos technique for nuclear response surfaces

For some years Lanczos moments methods have been combined with large-scale shell-model calculations in evaluations of the spectral distributions of certain operators. This technique is of great value because the alternative, a state-by-state summation over final states, is generally not feasible. The most celebrated application is to the Gamow-Teller operator, which governs beta decay and neutrino reactions in the allowed limit. The Lanczos procedure determines the nuclear response along a line q=0 in the (omega,q) plane, where omega and q are the energy and three-momentum transfered to the nucleus. However, generalizing such treatments from the allowed limit to general electroweak response functions at arbitrary momentum transfers seems considerably more difficult: the response function must be determined over the entire (omega,q) plane for an operator O(q) that is not fixed, but depends explicitly on q. Such operators arise in any semileptonic process where the momentum transfer is comparable to (or larger than) the inverse nuclear size. Here we show, for Slater determinants built on harmonic oscillator basis functions, that the nuclear response for any multipole operator O(q) can be determined efficiently over the full response plane by a generalization of the standard Lanczos moments method. We describe the Piecewise Moments Method and thoroughly explore its convergence properties for the test case of electromagnetic responses in a full sd-shell calculation of 28Si. We discuss possible extensions to a variety of electroweak processes, including charged- and neutral-current neutrino scattering.

M1and Gamow-Teller transitions inT=1/2nuclei23Naand23Mg

The magnetic dipole $(M1)$ operator consists not only of the usually dominant isovector (IV) spin $(\ensuremath{\sigma}\ensuremath{\tau})$ term, but also of IV orbital $(l\ensuremath{\tau}),$ isoscalar (IS) spin $(\ensuremath{\sigma}),$ and IS orbital (l) terms. On the other hand, the Gamow-Teller (GT) operator contains only the $\ensuremath{\sigma}\ensuremath{\tau}$ term. Under the assumption that isospin is a good quantum number, isobaric analog structure is expected in a pair of $T=1/2$ mirror nuclei, and thus analogous transitions are found. For the $M1$ transitions in the $T=1/2$ mirror nuclei pair ${}^{23}\mathrm{Na}{\ensuremath{-}}^{23}\mathrm{Mg},$ the contributions of these various terms have been studied by comparing the strengths of the analogous $M1$ $\ensuremath{\gamma}$ transitions and the GT transitions deduced from high-resolution ${}^{23}\mathrm{Na}{(}^{3}\mathrm{He}{,t)}^{23}\mathrm{Mg}$ charge-exchange measurements. In some $M1$ transitions, unusually large orbital contributions were observed even for strong transitions, while in some others, almost no orbital contribution was found. It is known that ${}^{23}\mathrm{Na}$ and ${}^{23}\mathrm{Mg}$ are deformed. The large difference of the orbital contributions is explained based on the different selection rules for l and $\ensuremath{\sigma}$ operators in transitions connecting different deformed bands. Precise excitation energies are determined for the states above the proton separation energy in ${}^{23}\mathrm{Mg}.$ These states are of astrophysical interest because of their important role played in the ${}^{22}\mathrm{Na}(p,\ensuremath{\gamma}{)}^{23}\mathrm{Mg}$ reaction of the Ne-Na cycle in nucleosynthesis.

Gamow-Teller strength distributions infp-shell nuclei

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 temperature.

Shell-model calculations for the properties of nuclei with A = 86–100 near the proton drip line

Extensive shell-model calculations in the mass range A = 86–100 on the neutron-deficient side of the nuclear chart are performed. The complete spectra of all isotopes are computed and compared to experimental excitation energies where available. Beta decay half lives are evaluated with both free and effective Gamow-Teller operators. The binding energies are obtained using a five parameter fit in addition to the shell-model energies. From the binding energies we deduce the proton drip line.

Double beta decay of92Mo: Comparison of the shell model and the quasiparticle random-phase approximation

The two-neutrino double beta decay of ${}^{92}$Mo to the ground state and excited states of ${}^{92}$Zr is analyzed using the shell-model approach and the quasiparticle random-phase approximation (QRPA). Two different valence spaces and three different Gamow-Teller operators are used in the shell-model analysis. The resulting double beta matrix elements and half-lives are compared with the corresponding QRPA results.

Beta decay of 44V.

We have calculated the [beta][sup +] decay of the proton-rich nuclei [sup 44]V in the full [ital fp]-shell valence space. Using the standard quenching factor 0.77 for the Gamow-Teller (GT) operator we obtain a theoretical half-life of 71 ms in good agreement with the experimental value [ital t][sub 1/2]=90[plus minus]25 ms. We also compute the Gamow-Teller strength functions corresponding to the decays of the 2[sup +] ground state and 6[sup +] isomer state. Our results indicate that 80% of the total GT strength falls within the [beta][sup +] energy window.

Shell-model calculation of the beta + decay of 98Cd, 96Pd and 94Ru

Shell-model calculations of the beta + decay of 94Ru, 96Pd and 98Cd are presented and compared to recent experiments. Two choices of model space are considered for the valence protons; the Og9/2 space and the Og9/2, 1p1/2 1p3/2 space. In addition the Gamow-Teller operator is renormalized by considering first-order corrections to the initial wavefunctions. It is shown that the combined effects of enlarging the model space and renormalizing the Gamow-Teller operator improve the agreement with experiment but still, with the exception of the 94Ru decay, the calculated hindrance factors are smaller than the observed ones.

Gamow-Teller beta-decay rates forA≤18 nuclei

A comprehensive analysis is made of the experimental information on Gamow-Teller beta decay for the light (A\ensuremath{\le}18) nuclei. Experimental data on half-lives, Q values, and branching ratios are tabulated. Experimental logft values and beta-decay matrix elements are deduced from these data. The one-body-transition densities necessary to predict the beta-decay matrix elements are then calculated using a recently constructed shell-model Hamiltonian operating in the first four major shells. Using these parameters, effective Gamow-Teller operators are deduced for the 0p shell from a least-squares fit to 16 experimental matrix elements. The effective operators are used to calculate 83 decay matrix elements. Some specific decays are discussed.

Gamow-Teller strength in the beta + decay of 37Ca.

Calculations are presented for the Gamow-Teller strength distribution in the ${\mathrm{\ensuremath{\beta}}}^{+}$ decay of $^{37}\mathrm{Ca}$ and compared to results extracted from recent beta decay data and from (p,n) data on the analog nucleus $^{37}\mathrm{Cl}$. The strength distribution is shown to be sensitive to the Hamiltonian, and comparison with experiment indicates a need for further improvement in the 1s0d shell Hamiltonian. It also indicates that the quenching of the Gamow-Teller operator in the upper part of the 1s0d shell is similar to that deduced from previous analyses.