Sum Rule Strength Research Articles

Isoscalar and isovector spin response in sd -shell nuclei

The spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions taking into accout enhanced isoscalar (IS) spin-triplet pairing as well as the effective spin operators. It was shown that the IS pairing and the effective spin operators gives a large quenching effect on the IV spin transitions to be consistent with observed data by $(p,p')$ experiments. On the other hand, the observed IS spin strength show much smaller quenching effect than expected by the calculated results. The IS pairing gives a substantial quenching effect on the spin magnetic dipole transitions, especially on the isovector (IV) ones. Consequently, an enhanced isoscalar spin-triplet pairing interaction enlarges the proton-neutron spin-spin correlation deduced from the difference between the isoscalar (IS) and the IV sum rule strengths. The beta-decay rates and the IS magnetic moments of $sd-$shell are also examined in terms of the IS pairing as well as the effective spin operators.

Effect of isoscalar spin-triplet pairings on spin-isospin responses in sd -shell nuclei

The spin magnetic dipole transitions and the neutron-proton spin-spin correlations in $sd-$shell even-even nuclei with $N=Z$ are investigated using shell model wave functions. The isoscalar spin-triplet pairing correlation provides a substantial quenching effect on the spin magnetic dipole transitions, especially the isovector (IV) ones. Consequently, an enhanced isoscalar spin-triplet pairing interaction influences the proton-neutron spin-spin correlation deduced from the difference between the isoscalar (IS) and the IV sum rule strengths. The effect of the $\Delta$ ($\Delta_{33}$ resonance)-hole coupling is examined in the IV spin transition and the spin-spin correlations of the ground states.

Gamma decay of pygmy states from inelastic scattering of ions

An overview of relevant results on the study of 1− states focusing on their excitation with nuclear probes is given. Results obtained for the 90Zr , 124Sn , and 208Pb nuclei using the (17O,17O′γ) reaction are compared with available data obtained with the (γ, γ′, and (p, p′) reactions. These comparisons allow to learn on the nature of the populated states, particularly the E1 states, whose isospin character is presently poorly known. The DWBA description of the data is discussed in terms of different form factors, standard collective form factor and form factors obtained by folding microscopically calculated transition densities. The relevant aspects related to the used theoretical approach are also presented. The main objective of the analyses is the extraction of the values of the fraction of the energy weighted sum rule strength for the isoscalar dipole excitation. For completeness, in all cases, the DWBA analysis was made also for the excitations of 2+ and 3− states.

Dipole response of neutron-rich Sn isotopes

The neutron-rich isotopes 129–133Sn were studied in a Coulomb excitation experiment at about 500 AMeV using the FRS-LAND setup at GSI. From the exclusive measurement of all projectile-like particles following the excitation and decay of the projectile in a high-Z target, the energy differential cross section can be extracted. At these beam energies dipole transitions are dominating, and within the semi-classical approach the Coulomb excitation cross sections can be transformed into photoabsorption cross sections. In contrast to stable Sn nuclei, a substantial fraction of dipole strength is observed at energies below the giant dipole resonance (GDR). For 130Sn and 132Sn this strength is located in a peak-like structure around 10 MeV excitation energy and exhibits a few percent of the Thomas-Reiche Kuhn (TRK) sum-rule strength. Several calculations predict the appearance of dipole strength at low excitation energies in neutron-rich nuclei. This low-lying strength is often referred to as pygmy dipole resonance (PDR) and, in a macroscopic picture, is discussed in terms of a collective oscillation of excess neutrons versus the core nucleons. Moreover, a sharp rise is observed at the neutron separation threshold around 5 MeV for the odd isotopes. A possible contribution of 'threshold strength', which can be described within the direct-breakup model is discussed. The results for the neutron-rich Sn isotopes are confronted with results on stable nuclei investigated in experiments using real photons.

Isospin asymmetry in the continuum of the A = 14 mirror nuclei

We study the isospin asymmetry in the isoscalar (IS) excitations in the mirror nuclei 14O and 14C by using the Hartree–Fock(HF)+random phase approximation (RPA) linear response function theory with a Skyrme interaction to take into account the continuum effect properly. The asymmetry in the IS monopole, dipole responses is pointed out in the continuum near the particle threshold with respect to the excitation energy and the sum rule strength. On the other hand, no clear sign of the asymmetry is found in the giant resonance (GR) region. In the quadrupole case, the calculated strengths of the mirror nuclei show almost the same energy dependence from the threshold to the GR region. It is found that the transition densities of the monopole response show an extended halo structure near the threshold, while those of the GR region show a typical radial dependence of the compressional collective mode without any halo effect. Contrary to the transition densities of the monopole response, those of quadrupole response do not show any sign of the extended feature of wavefunctions neither near the threshold nor the GR energy region. Calculated strength distributions of the IS multipole states are compared with recent experimental data obtained by the multipole decomposition analysis of α inelastic scattering on 14O.

Collective excitations close to the particle threshold

We report on photon scattering ( γ , γ ′ ) experiments to measure the detailed dipole strength distribution between about 3 and 10 MeV in the Z = 20 Ca isotopic chain and in N = 82 nuclei. A concentration of electric dipole strength carrying a considerable part of the total E1 sum rule strength is observed in all examined nuclei below the particle threshold. The experimental results are compared to theoretical predictions and future approaches to study the excitation mode are discussed.

Excitation and decay of the isovector spin-flip giant monopole resonance via thePb(He,) reaction at 410 MeV

The excitation and subsequent decay by proton emission of the isovector spin-flip giant monopole resonance are studied via the208Pb(3He,t) reaction at 410 MeV. In the triton-singles spectrum 60 ± 5% of the non-energy-weighted sum-rule strength for this 2ħω resonance is found in the region29 < Ex(208Bi) < 51 MeV. The central excitation energy and width of the IVSGMR are determined to be 37 ± 1 MeV and 14 ± 3 MeV, respectively.

Excitation and decay of the isovector spin-flip giant monopole resonance via the 208Pb( 3He, tp) reaction at 410 MeV

The excitation and subsequent decay by proton emission of the isovector spin-flip giant monopole resonance are studied via the 208Pb( 3He, t) reaction at 410 MeV. In the triton-singles spectrum 60 ± 5% of the non-energy-weighted sum-rule strength for this 2ħω resonance is found in the region 29 < E x ( 208Bi) < 51 MeV. The central excitation energy and width of the IVSGMR are determined to be 37 ± 1 MeV and 14 ± 3 MeV, respectively.

Excitation and decay of the isovector giant monopole resonances via the 208Pb(3He,t p) reaction at 410 MeV.

The excitation and subsequent proton decay of the isovector spin-flip giant monopole resonance (IVSGMR) is studied via the 208Pb(3He,t) reaction at 410 MeV. In the inclusive spectrum (60+/-5)% of the non-energy-weighted sum-rule strength for this 2 variant Planck's over 2h omega resonance was found in the region 29<Ex(208Bi)<51 MeV. The central excitation energy and width of the IVSGMR are 37+/-1 MeV and 14+/-3 MeV, respectively. It is found that the branching ratio for proton decay is (52+/-12)% and that the deep neutron-hole states in 207Pb are strongly fed.

Structure and Reaction Studies of Loosely Bound Nuclei Using Radioactive Nuclear Beams

Coulomb breakup of neutron-rich nuclei around mass A ∼ 20 has been studied experimentally using secondary beams (∼ 500–600 MeV/u) of unstable nuclei produced at GSI. The spectroscopic factors deduced for the neutron occupying s1/2 level in 15C and 14B ground state is consistent with the earlier reported values. The data analysis for Coulomb breakup of 17C shows that most of the cross section yields the 16C core in its excited state. For 17-22O, the low-lying E1 strength amounts up to about 12% of the energy weighted dipole sum rule strength depending on neutron excess.

Measurement of the dipole response of neutron-rich nuclei in the A∼20 region

Coulomb break up of the neutron-rich 15,17C and 17–22O isotopes has been studied experimentally using secondary beams at energies of 500–600 MeV/u. A comparison between differential cross sections, dσ/ dE ∗ , with that obtained from a binary model shows that the main ground-state configuration of 15C is 14C(0 +)⊗ ν S 1/2 as expected. For 17C, our preliminary data analysis reveals that the predominant (∼64%) configuration of the ground state is 16C(2 +)⊗ ν s, d . For 17–22O, the low-lying E1 strength amounts up to about 12% of the energy weighted sum rule strength depending on neutron number. The energy weighted E1 strength (integrated up to 15 MeV excitation energy) increases up to 20O then decreases for 21,22O. These data are compared to a shell model calculation.

Structure of light neutron-rich nuclei through coulomb dissociation

Coulomb breakup of neutron-rich nuclei around mass A ∼ 20 has been studied experimentally using secondary beams (∼ 500–600 MeV/u) of unstable nuclei produced at GSI. The spectroscopic factor deduced for the neutron occupying s 1/2 level in 15C ground state is consistent with the earlier reported value. The data analysis for Coulomb breakup of 17C shows that most of the cross section yields the 16C core in its excited state. For 17–22O, the low-lying E1 strength amounts up to about 12% of the energy weighted dipole sum rule strength depending on neutron excess. The cluster sum rule limit with 16O as a core is almost exhausted for 17,18O, while for more neutron rich isotopes the strength with respect to that limit decreases.

Excitation of Isovector Spin-Dipole Resonances and Neutron Skin of Nuclei

The cross sections of the isovector spin-dipole resonances (SDR) in the Sb isotopes excited by the ${(}^{3}\mathrm{He},t)$ charge-exchange reaction at 450 MeV for $0\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\le}{\ensuremath{\theta}}_{t}\ensuremath{\le}1.15\ifmmode^\circ\else\textdegree\fi{}$ have been measured. The results are compared with the predicted sum-rule strengths related to the difference of neutron and proton root-mean-square radii. Within the model used, the radii differences (neutron-skin thicknesses) deduced for ${}^{114}\mathrm{Sn}$, ${}^{116}\mathrm{Sn}$, ${}^{118}\mathrm{Sn}$, ${}^{122}\mathrm{Sn}$, and ${}^{124}\mathrm{Sn}$ are $\ensuremath{\le}0.09$, $0.12\ifmmode\pm\else\textpm\fi{}0.06$, $0.13\ifmmode\pm\else\textpm\fi{}0.06$, $0.22\ifmmode\pm\else\textpm\fi{}0.07$, and $0.19\ifmmode\pm\else\textpm\fi{}0.07\mathrm{fm}$, respectively. This result suggests a new method for the measurement of the neutron-skin thicknesses of unstable nuclei.

Folding model analysis of the excitation of low-lying states and the high energy octupole resonance in116Snby 240 MeV α scattering

The sum rule strength of the high energy octupole resonance (HEOR) and the transition rates of low-lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states of ${}^{116}\mathrm{Sn},$ excited by 240 MeV \ensuremath{\alpha} scattering, have been determined from deformed potential and folding model analyses. Deformed potential cross sections for both the low-lying ${3}^{\ensuremath{-}}$ state and the HEOR are greater than folding cross sections by a factor of 1.18. The high energy octupole resonance was found to exhaust $(70\ifmmode\pm\else\textpm\fi{}15)%$ and $(83\ifmmode\pm\else\textpm\fi{}15)%$ of the $E3$ energy-weighted sum rule from the two analyses, respectively. The data for the low-lying states are fit well by the calculations made with both models using electromagnetic values for the transition rates. Optical-model parameters were obtained from fits to elastic scattering data. The differential cross sections for the elastic scattering and inelastic scattering exciting the low-lying ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in ${}^{116}\mathrm{Sn}$ were measured over the angle range from ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=1.6\ifmmode^\circ\else\textdegree\fi{}$ to 35.2\ifmmode^\circ\else\textdegree\fi{}.

Invariant-mass spectroscopy of 10Li and 11Li

Break-up of secondary 11Li ion beams (280 MeV/nucleon) on C and Pb targets into 9Li and neutrons is studied experimentally. Cross sections and neutron multiplicity distributions are obtained, characterizing different reaction mechanisms. Invariant-mass spectroscopy for 11Li and 10Li is performed. The E1 strength distribution, deduced from electromagnetic excitation of 11Li up to an excitation energy of 4 MeV comprises ∼8% of the Thomas-Reiche-Kuhn energy-weighted sumrule strength. Two low-lying resonance-like structures are observed for 10Li at decay energies of 0.21(5) and 0.62(10) MeV, the former one carrying 26(10)% of the strength and likely to be associated with an s-wave neutron decay. A strong di-neutron correlation in 11Li can be discarded. Calculations in a quasi-particle RPA approach are compared with the experimental results for 10Li and 11Li.

Monopole resonance strengthsin58Niand208Pb

Giant monopole resonance strengths were obtained from small angle inelastic alpha scattering ${\mathrm{on}}^{58}$Ni ${\mathrm{and}}^{208}$Pb using deformed potential and folding models. Folding model analyses increase the sum rule strength in both nuclei, with 160% of the E0 sum rule required to fit the 13.7-MeV state in Pb. Significant contributions from other multipolarities could be excluded. The E0 strength identified ${\mathrm{in}}^{58}$Ni is shown to be about 42% of that identified ${\mathrm{in}}^{208}$Pb.

Giant dipole resonance in very hot nuclei of mass A

Gamma rays, light charged particles, and evaporation residues emitted from hot nuclei formed in the Ar36+90Zr reaction at 27 MeV/nucleon have been measured at the GANIL facility with the 4π barium fluoride multidetector MEDEA. The combination of the residue and particle measurements shows that nuclei with masses around 115 and excitation energies between 350 and 550 MeV are produced. The γ spectra measured in coincidence with the evaporation residues exhibit three components: a low-energy statistical component, a high-energy contribution due to nucleon-nucleon bremsstrahlung during the initial stages of the collision, and a contribution from the decay of the giant dipole resonance built on highly excited states. The characteristics of the bremsstrahlung component are in agreement with previously published systematics. The γ yield from the decay of the giant dipole resonance remains constant over the excitation energy range studied. A comparison with other experiments shows that the N/Z asymmetry in the entrance channel does not affect the γ yield. Statistical calculations performed using the code CASCADE and supposing a fixed width and full sum rule strength for the dipole resonance strongly overpredict the data. The hypothesis of a continuously increasing width of the resonance with temperature gives a better agreement with experiment near the centroid of the resonance but overpredicts the γ spectra at higher energies. The best account of the data is given by assuming a cutoff of γ emission from the resonance above an excitation energy of approximately 250 MeV. This cutoff is discussed in terms of the time necessary to equilibrate the dipole oscillations with the hot compound nucleus. Finally, some evidence is given for a possible new low-energy component of the dipole strength at very high temperatures. © 1996 The American Physical Society.Received 8 December 1995DOI:https://doi.org/10.1103/PhysRevC.53.2258©1996 American Physical Society

Bivariate distributions in statistical spectroscopy studies: IV. Interacting particle Gamow-Teller strength densities and ?-decay rates offp-shell nuclei for presupernova stars

A method to calculate temperature dependentβ-decay rates is developed by writing the expression for the rates explicitly in terms of bivariateGT strength densities (I (GT)) for a given hamiltonianH=h+V and state densities of the parent nucleus besides having the usual phase space factors. The theory developed in the preceding paper (III) for constructing NIP strength densities is applied for generatingI (GT) and thenI (GT) is constructed using the bivariate convolution formI (GT)=Σ S I ⊗ρ V, ; BIV-G . The spreading bivariate Gaussian ρ V ;BIV-G, forfp-shell nuclei, is constructed by assuming that the marginal centroids are zero, the marginal variances are same as the corresponding state density variances and fixing the bivariate correlation coefficient $$\bar \zeta $$ using experimentalβ-decay half lifes. With the deduced values of $$\bar \zeta $$ $$\bar \zeta $$ ∼ 0.67,β-S-decay rates for61,62Fe and62–64Co isotopes are calculated at presupernova matter densitiesρ=107–109 gm/cc, temperaturesT=(3–5)×109 ∘K and electron fractions Ye=0.43–0.5. The convolution form forI O(GT) led to a simple expression for calculatingGT non-energy weighted sum rule strength and it describes (within 10%) the shell model results offp-shell nuclei.

Structure of unstable nuclei near proton drip line

Abstract Gamov-Teller (GT) states in nuclei near the proton drip line are studied by using a microscopic Hartree-Fock (H-F) + Tamm-Dancoff approximation (TDA) (or random phase approximation (RPA)). The calculations predict that giant Gamow-Teller (GT) β-decays are possible for N=Z nuclei heavier than 28 56 Ni 28 , carrying most of the sum rule strength. The amplitude of isospin T=1 admixed to the T=0 ground state in N=Z nuclei is also discussed in relation with Fermi β-decay sum rule. Finally, the shapes of unstable nuclei near the proton drip line are studied by using the finite-range droplet model (FRDM).

Perspectives on study of unstable nuclei near drip lines

We discussed several structure problems of nuclei both near the neutron and the proton drip lines. The conditions for the growth of halo nucleus are discussed together with experimental evidence of neutron and proton halos. Next, a microscopic Hartree-Fock (HF) + random phase approximation (RPA) model is applied to calculate dipole excitations in halo nuclei, and the results are compared with experimental data in 11Be. It is pointed out that the abnormally large dipole strength is accumulated by the threshold effect inherent to halo nuclei. Giant Gamow-Teller (GT) states in nuclei near the proton drip line is also studied by using the same microscopic model. The nuclei with Z28 are predicted to have giant GT beta decays which carry most of the sum rule strength.