Gamow-Teller Giant Resonance Research Articles

Energy-weighted sum rule for Gamow-Teller giant resonances in high-spin isomeric states of N=Z nuclei

The sum-rule approach and the shell model are used to estimate the energies of Gamow-Teller (GT) giant resonances in high-spin isomeric (HSI) states in $N=Z$ nuclei. The newly derived energy-weighted sum rules show that the GT resonance energies of HSI states are related to the $\ensuremath{\sigma}\ensuremath{\sigma}\ensuremath{\tau}\ensuremath{\tau}$ and $\ensuremath{\sigma}\ensuremath{\sigma}$ interactions. Comparing the results of the sum-rule approach with those of large-scale shell-model calculations for the $^{52}\mathrm{Fe}({12}^{+})$ and $^{94}\mathrm{Ag}({21}^{+})\phantom{\rule{4pt}{0ex}}N=Z$ high-spin isomers, the deduced ${\ensuremath{\kappa}}_{\ensuremath{\sigma}}$, which is the strength of the $\ensuremath{\sigma}\ensuremath{\sigma}$ residual interaction in a simple residual-interaction model, is 2.5 MeV.

Effect of High-Lying Resonances on Cross Sections for Solar-Neutrino Capture by $${}^{\mathbf{127}}$$I Nuclei

The resonance structure of the charge-exchange strength function $$S(E)$$ and its effect on the cross sections for solar-neutrino capture by $${}^{127}$$ I nuclei are analyzed. Three types of isobaric resonances are studied within the self-consistent theory of finite Fermi systems. These are the giant Gamow–Teller resonance; the analog resonance; and the pygmy resonances, which lie lower. The capture cross section $$\sigma(E)$$ for solar neutrinos incident to $${}^{127}$$ I nuclei is calculated with allowance for the resonance structure of the strength function $$S(E)$$ , and the effect of each resonance on the energy dependence $$\sigma(E)$$ is analyzed. It is shown that all high-lying charge-exchange resonances should be taken into account in calculating the cross section $$\sigma(E)$$ . The contributions of neutrinos of different origin to the structure of the cross section $$\sigma(E)$$ are analyzed. In particular, the contribution of energetic neutrinos to the ratio of the $${}^{127}$$ Xe and $${}^{126}$$ Xe production rates is considered. The $${}^{126}$$ Xe $$/^{127}$$ Xe isotope ratio is an indicator of hard boron neutrinos in the solar spectrum.

Cross Section of Solar Neutrino Capture by 76Ge Nuclei

The results are presented from calculating capture cross section σ(Eν) of solar neutrinos by 76Ge nuclei. Experimental data on strength function S(E), obtained in the charge-exchange 76Ge(3He, t)76As reaction, are used in these calculations. The effect the resonance structure of strength function S(E) has on cross section σ(Eν) is examined. It is shown that the giant Gamow–Teller resonance alone makes a contribution of ~20%, and the contribution of lower-lying excitations in the continuous spectrum part is even larger. These contributions must be considered in calculations for background events in experiments on double beta decay of the GERDA (LEGEND) type.

Extraction of the Landau-Migdal Parameter from the Gamow-Teller Giant Resonance in ^{132}Sn.

The key parameter to discuss the possibility of the pion condensation in nuclear matter, i.e., the so-called Landau-Migdal parameter g^{'}, was extracted by measuring the double-differential cross sections for the (p,n) reaction at 216 MeV/u on a neutron-rich doubly magic unstable nucleus, ^{132}Sn with the quality comparable to data taken with stable nuclei. The extracted strengths for Gamow-Teller (GT) transitions from ^{132}Sn leading to ^{132}Sb exhibit the GT giant resonance (GTR) at the excitation energy of 16.3±0.4(stat)±0.4(syst) MeV with the width of Γ=4.7±0.8 MeV. The integrated GT strength up to E_{x}=25 MeV is S_{GT}^{-}=53±5(stat)_{-10}^{+11}(syst), corresponding to 56% of Ikeda's sum rule of 3(N-Z)=96. The present result accurately constrains the Landau-Migdal parameter as g^{'}=0.68±0.07, thanks to the high sensitivity of the GTR energy to g^{'}. In combination with previous studies on the GTR for ^{90}Zr and ^{208}Pb, the result of this work shows the constancy of this parameter in the nuclear chart region with (N-Z)/A=0.11 to 0.24 and A=90 to 208.

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.

Systematic shell-model study of β -decay properties and Gamow-Teller strength distributions in A≈40 neutron-rich nuclei

We perform large-scale shell-model calculations of $\ensuremath{\beta}$-decay properties for neutron-rich nuclei with $13\ensuremath{\le}Z\ensuremath{\le}18$ and $22\ensuremath{\le}N\ensuremath{\le}34$, taking the first-forbidden transitions into account. The natural-parity and unnatural-parity states are calculated in the $0\ensuremath{\hbar}\ensuremath{\omega}$ and $1\ensuremath{\hbar}\ensuremath{\omega}$ model spaces, respectively, within the full $sd+pf+sdg$ valence shell. The calculated $\ensuremath{\beta}$-decay half-lives and $\ensuremath{\beta}$-delayed neutron emission probabilities show good agreement with the experimental data. The first-forbidden transitions make a non-negligible contribution to the half-lives of $N\ensuremath{\gtrsim}28$ nuclei. The low-lying Gamow-Teller strengths of even-even nuclei are considerably larger than those of the neighboring odd-$A$ and odd-odd nuclei, strongly affecting the half-lives and neutron emission probabilities. It is shown that this even-odd effect is caused by the ${J}^{\ensuremath{\pi}}={1}^{+}$ proton-neutron pairing interaction. We derive a formula to represent the positions of the Gamow-Teller giant resonances from the calculated strength distributions.

The “Folk Theorem” on effective field theory: How does it fare in nuclear physics?

This is a brief history of what I consider as very important, some of which truly seminal, contributions made by young Korean nuclear theorists, mostly graduate students working on PhD thesis in 1990s and early 2000s, to nuclear effective field theory, nowadays heralded as the first-principle approach to nuclear physics. The theoretical framework employed is an effective field theory anchored on a single scale-invariant hidden local symmetric Lagrangian constructed in the spirit of Weinberg’s “Folk Theorem” on effective field theory. The problems addressed are the high-precision calculations on the thermal np capture, the solar pp fusion process, the solar hep process — John Bahcall’s challenge to nuclear theorists — and the quenching of g A in giant Gamow-Teller resonances and the whopping enhancement of first-forbidden beta transitions relevant in astrophysical processes. Extending adventurously the strategy to a wild uncharted domain in which a systematic implementation of the “theorem” is far from obvious, the same effective Lagrangian is applied to the structure of compact stars. A surprising, unexpected, result on the properties of massive stars, totally different from what has been obtained up to day in the literature, is predicted, such as the precocious onset of conformal sound velocity together with a hint for the possible emergence in dense matter of hidden symmetries such as scale symmetry and hidden local symmetry.

Charge-exchange pigmy resonances of tin isotopes

Charge-exchange states, the so-called “pigmy” resonances, which are below the giant Gamow–Teller resonance, have been studied in the self-consistent theory of finite Fermi systems. Microscopic numerical calculations and semiclassical calculations are presented for nine tin isotopes with the mass numbers A =112, 114, 116, 117, 118, 119, 120, 122, and 124, for which experimental data exist. These data have been obtained in the Sn(3He,t)Sb charge-exchange reaction at the energy E(3He) = 200 MeV. The comparison of calculations with experimental data on the energies of charge-exchange resonances gives the standard deviation δE < 0.40 MeV for microscopic numerical calculations and δE < 0.55 MeV for calculations by semiclassical formulas, which are comparable with experimental errors. The strength function for the 118Sn isotope has been calculated. It has been shown that the calculated resonance energies are close to the experimental values; the calculated and experimental relations between heights of pygmy resonance peaks are also close to each other.

Charge-exchange resonances and restoration of Wigner’s supersymmetry in heavy and superheavy nuclei

Various facets of the question of whether Wigner’s supersymmetry [SU(4) symmetry] may be restored in heavy and superheavy nuclei are analyzed on the basis of a comparison of the results of calculations with experimental data. The energy difference between the giant Gamow–Teller resonance and the analog resonance (the difference of E G and E A) according to calculations based on the theory of finite Fermi systems is presented for the case of 33 nuclei for which experimental data are available. The calculated difference ΔE G–A of E G and E A tends to zero in heavier nuclei, showing evidence of the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring isobaric nuclei is analyzed within the SU(4) approach for more than 400 nuclei in the mass-number range of A = 5–244. The restoration of Wigner’s SU(4) symmetry in heavy nuclei is confirmed. It is shown that the restoration of SU(4) symmetry is compatible with the possible existence of the stability island in the region of superheavy nuclei.

Estimation of a 2p2h effect on Gamow-Teller transitions within the second Tamm-Dancoff approximation

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 $^{24}\mathrm{O}$ and $^{34}\mathrm{Si}$ and stable $^{48}\mathrm{Ca}$ nuclei are chosen to study the quenching and fragmentation of the GT strengths. Correlation of the 2p2h configurations causes about $20%$ quenching and downward shift of GT giant resonances (GTGRs). The residual interaction changing relative angular momentum that appeared in the tensor force part gives a meaningful effect to the GT strength distributions. In this work, $17--26%$ of the total GT strengths are brought to high-energy region above GTGRs. In particular, the tensor force brings strengths to high energy more than 50 MeV. STDA calculation within a small model space for 2p2h configuration is also performed and experimental data of $^{48}\mathrm{Ca}$ is reproduced reasonably.

A microscopic approach based on particle-vibration coupling: application to charge-exchange transitions and multiplets in odd nuclei

In this contribution, we shall describe a formalism that goes beyond the simple time-dependent mean field and is based on particle-vibration coupling (PVC). Such a formalism has been developed with the idea of being self-consistent. It makes use of Skyrme effective forces, and has been used for several applications. We will focus on charge-exchange transitions, namely we will show that our model describes well both the Gamow-Teller giant resonance width, and the low-lying transitions associated with β -decay. In this latter case, including PVC produces a significant improvement of the half-lives obtained at mean-field level, and leads to a good agreement with experimental data. We will end by discussing particle-phonon multiplets in odd nuclei.

Restoration of Wigner supersymmetry in heavy and superheavy nuclei

The possibility of the restoration of Wigner supersymmetry (SU(4) symmetry) in heavy and superheavy nuclei has been analyzed by comparing the calculations with experimental data. The differences between the energies of the giant Gamow–Teller resonance (EG) and analog resonance (EA) calculated within the finite Fermi system theory for 33 nuclei for which experimental data exist are presented. The energy differences ΔEG–A between EG and EA tend to zero in heavier nuclei, demonstrating the restoration of Wigner SU(4) symmetry. The energy differences ΔEG–A have also been calculated for heavy and superheavy nuclei located on the betastability line in the mass number range of A = 140–290. In the SU(4) approach, the isotopic dependence of the difference between the Coulomb energies of neighboring isobar nuclei has been analyzed for more than 400 nuclei in the mass number range of A = 3–244. The restoration of Wigner SU(4) symmetry in heavy and superheavy nuclei has been confirmed. It has been shown that the restoration of SU(4) symmetry does not contradict the possibility of the existence of the “island of stability” in the region of superheavy nuclei.

Effective axial-vector strength and β-decay systematics

We use the weak axial-vector coupling strength as a key parameter to reproduce simultaneously the available data for both the Gamow-Teller and decay rates in nine triplets of isobars with mass numbers . We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with schematic dipole interaction containing particle-particle and particle-hole parts with mass-dependent strengths. Our analysis points to a strongly quenched effective value , with a relative error of 28%. We then perform a systematic computation of 218 experimentally known and decays with quite a remarkable success. The presently extracted value of should be taken as an effective one, specific for a given nuclear theory framework. Present studies suggest that the effective is suitable for the description of decay transitions to states at moderate excitation, below the Gamow-Teller giant resonance region.

Spin-isospin response of deformed neutron-rich nuclei in a self-consistent Skyrme energy-density-functional approach

We develop a new framework of the self-consistent deformed proton-neutron quasiparticle-random-phase approximation (pnQRPA), formulated in the Hartree-Fock-Bogoliubov (HFB) single-quasiparticle basis. The same Skyrme force is used in both the HFB and pnQRPA calculations except in the proton-neutron particle-particle channel, where an S=1 contact force is employed. Numerical application is performed for Gamow-Teller (GT) strength distributions and $\beta$-decay rates in the deformed neutron-rich Zr isotopes located around the path of the rapid-neutron-capture process nucleosynthesis. It is found that the GT strength distributions are fragmented due to deformation. Furthermore we find that the momentum-dependent terms in the particle-hole residual interaction leads to a stronger collectivity of the GT giant resonance. The T=0 pairing enhances the low-lying strengths cooperatively with the T=1 pairing correlation, which shortens the $\beta$-decay half lives by at most an order of magnitude. The new calculation scheme reproduces well the observed isotopic dependence of the $\beta$-decay half lives of deformed $^{100-110}$Zr isotopes.

Complete sets of polarization transfer observables for the208Pb(p⃗,n⃗)reaction at 296 MeV and Gamow-Teller and spin-dipole strengths for208Pb

We report measurements of cross sections and analyzing powers for reaction angles of ${\ensuremath{\theta}}_{\mathrm{lab}}={0.0}^{\ensuremath{\circ}}$--${10.0}^{\ensuremath{\circ}}$ and complete sets of polarization transfer observables and induced polarizations at ${\ensuremath{\theta}}_{\mathrm{lab}}={0.0}^{\ensuremath{\circ}}$--${7.0}^{\ensuremath{\circ}}$ for the ${}^{208}\mathrm{Pb}(\stackrel{P\vec}{p},\stackrel{P\vec}{n})$ reaction at a bombarding energy of ${T}_{p}=296$ MeV. A multipole decomposition technique was applied to the data to extract the Gamow-Teller (GT) and spin-dipole (SD) components from the continuum. The polarization observables were also used, for the first time, to separate the SD components into different spin-parity transfer ($\ensuremath{\Delta}{J}^{\ensuremath{\pi}}={0}^{\ensuremath{-}}$, ${1}^{\ensuremath{-}}$, and ${2}^{\ensuremath{-}}$) contributions. A significant strength with $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}={1}^{+}$ is identified in the continuum beyond the GT giant resonance, which is due to configuration mixing effects and the isovector spin monopole (IVSM) contribution. The SD strength distributions were clearly dependent on $\ensuremath{\Delta}{J}^{\ensuremath{\pi}}$, which is reasonably reproduced by Hartree-Fock (HF) plus random phase approximation (RPA) calculations that include the Skyrme interaction with tensor components [Phys. Rev. C 83, 054316 (2011)].

Problems of experimental and theoretical studies of the Gamow-Teller giant resonance in118Sb

Properties of the Gamow-Teller giant resonance (GTGR) in 118 Sb are described within the semi- microscopic approach based on the extended version of the charge-exchange continuum-quasiparticle- random-phase-approximation and phenomenological treatment of the spreading effect. The structure effect of the configuration splitting of this GTGR is confirmed. With taking this effect into account the experimental data on excitation of the GTGR in direct and resonance reactions are analyzed.

On direct proton decay of the Gamow-Teller giant resonance

The semi-microscopic approach to the description of giant resonances in medium-heavy mass closed-shell nuclei is implemented to treat partial probabilities of direct-proton decay of the Gamow-Teller giant resonance (GTGR) in 208 Bi. The corresponding experimental data are reasonably explained.

Giant Gamow-Teller resonance: 40 Years after the prediction

A brief survey of the physics of the giant Gamow-Teller resonance, from the history of its prediction and the first attempts at theoretically describing it to the present-day state of this realm of nuclear physics, is given. The structure of Gamow-Teller resonances is analyzed within the theory of finite Fermi systems. Simple expressions for the energy of the Gamow-Teller resonance and for the matrix elements of its excitation are derived via approximately solving the equations of this theory by the semiclassical method. The calculated values of the energy difference between the Gamow-Teller resonance and the analogous resonance are found to be in good agreement with their experimental counterparts. Strength functions for the beta decay of neutron-rich nuclei, Sβ(E), are analyzed, and the calculated values of Sβ(E) are contrasted against relevant experimental data.

Erratum to: “Giant Gamow-Teller Resonance in Neutron-Rich Nuclei”

Nucleus Experiment Our present calculation T1/2, ms P1n P2n T1/2, ms P1n P2n P3n P2n/Pn+n Na 17 37.3 ± 5.4 1.15 ± 0.25 21 24.9 0.45 0.03 0.058 Na 12.9 23.9 ± 6.8 0.87 ± 0.24 10.6 23.8 3.4 0.08 0.12 Na 8.4 52 ± 20 8.3 ± 2.1 7.5 50.0 13.9 0.29 0.09 Na 5.5 113 ± 22∗ 12 ± 5 4.8 42.3 39.7 1.05 0.16 124.8∗ ∗ The summed value is the total number of neutrons, In = ∑ k kPkn, emitted per 100 β-decay events.

Giant Gamow-Teller resonance in neutron-rich nuclei

The giant Gamow-Teller resonance and other branches of collective nuclear excitations are described on the basis of the theory of finite Fermi systems. A connection between the Gamow-Teller resonance and Wigner SU(4) symmetry is proven. The beta-decay strength function and processes accompanying the β − decay of neutron-rich nuclei are described. The effect of the satellites of the Gamow-Teller resonance on the decay properties of neutron-rich nuclei is analyzed.