Strength In Nuclei Research Articles

Electric and magnetic dipole strength inSn112,114,116,118,120,124

Background: There is renewed interest in electric dipole strength distributions for a variety of reasons including the extraction of the dipole polarizability related to properties of the symmetry energy and a measure for the neutron skin thickness, understanding the structure of low-energy E1 strength in nuclei with neutron excess, and establishing the systematics of the isovector giant dipole resonance (IVGDR). Inelastic proton scattering at energies of a few hundred MeV and very forward angles including 0∘ has been established as a tool for the study of electric and magnetic dipole strength distributions in nuclei. Purpose: The present work aims at a systematic investigation of the electric and magnetic dipole strength distributions in the chain of stable even-mass tin isotopes. Methods: Inelastic proton scattering experiments were performed at the Research Center for Nuclear Physics, Osaka, with a 295-MeV beam covering laboratory angles 0∘–6∘ and excitation energies 6–22 MeV. Cross sections due to E1 and M1 excitations were extracted with a multipole decomposition analysis (MDA) and then converted to reduced transition probabilities with the “virtual photon method” for E1 and the “unit cross section method” for M1 excitations, respectively. Including a theory-aided correction for the high-excitation-energy region not covered experimentally, the electric dipole polarizability was determined from the E1 strength distributions. Results: Total photoabsorption cross sections derived from the E1 and M1 strength distributions show significant differences compared to those from previous (γ,xn) experiments in the energy region of the IVGDR. The widths of the IVGDR deduced from the present data with a Lorentz parametrization show an approximately constant value of about 4.5 MeV in contrast to the large variations between isotopes observed in previous work. The IVGDR centroid energies are in good correspondence to expectations from empirical systematics of their mass dependence. Furthermore, a study of the dependence of the IVGDR energies on bulk matter properties is presented. The E1 strengths below neutron threshold show fair agreement with results from (γ,γ′) experiments on Sn112,116,120,124 in the energy region between 6 and 7 MeV, where also isoscalar E1 strength was found for Sn124. At higher excitation energies, large differences are observed, pointing to a different nature of the excited states with small ground-state branching ratios. The isovector spin-M1 strengths exhibit a broad distribution between 6 and 12 MeV in all studied nuclei. Conclusions: The present results contribute to the solution of a variety of nuclear structure problems including the systematics of the energy and width of the IVGDR, the structure of low-energy E1 strength in nuclei, new constraints to energy density functionals (EDFs) aiming at a systematic description of the dipole polarizability across the nuclear chart, from which properties of the symmetry energy can be derived, and the systematics of the isovector spin-M1 strength in heavy nuclei.16 MoreReceived 12 July 2020Accepted 2 September 2020DOI:https://doi.org/10.1103/PhysRevC.102.034327©2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective levelsElectromagnetic transitionsH & He induced nuclear reactionsNuclear density functional theoryNuclear structure & decaysPhotonuclear reactionsNuclear Physics

Interplay between low-lying isoscalar and isovector dipole modes: A comparative analysis between semiclassical and quantum approaches

We perform Time Dependent Hartree-Fock (TDHF) calculations to investigate the small amplitude dipole response of selected neutron-rich nuclei and Sn isotopes. A detailed comparison with the dipole strength predicted by Random-Phase Approximation (RPA) calculations is presented for the first time. TDHF results are also confronted to Vlasov calculations, to explore up to which extent a semi-classical picture can explain the properties of the nuclear response. The focus is on the low-energy response, below the Giant Dipole Resonance region, where different modes of non negligible strength are identified. We show that the relative weight of these excitations evolves with nuclear global features, such as density profile and neutron skin, which in turn reflect impor tant properties of the nuclear effective interaction. A thorough analysis of the associated transition densities turns out to be quite useful to better characterize the mixed isoscalar(IS)/isovector(IV) nature of the different modes and their surface/volume components. In particular, we show that the dipole response in the so-called Pygmy Dipole Resonance region corresponds to isoscalar-like surface oscillations, of larger strength in nuclei with a more diffuse surface. The ratio between the IV and IS Energy Weighted Sum Rule fractions exhausted in this region is shown to almost linearly increase with the neutron skin thickness in Sn isotopes.

Erratum: Many-body interactions of neutrinos with nuclei: Observables [Phys. Rev. C86, 014614 (2012)

Background: The total inclusive cross sections obtained for quasielastic (QE) scattering in the Mini Booster Neutrino Experiment (MiniBooNE) are significantly larger than those calculated by all models based on the impulse approximation and using the world average value for the axial mass of $M_A \approx 1 \GeV$. This discrepancy has led to various, quite different explanations in terms of increased axial masses, changes in the functional form of the axial form factor, increased vector strength in nuclei, and initial two-particle interactions. This is disconcerting since the neutrino energy reconstruction depends on the reaction mechanism. Purpose: We investigate whether exclusive observables, such as nucleon knock-out, can be used to distinguish between the various proposed reaction mechanisms. We determine the influence of 2p-2h excitations on the energy reconstruction. Method: We use the Giessen Boltzmann--Uehling--Uhlenbeck (GiBUU) model to predict numbers and spectra of knock-out nucleons. The model is extended by incorporating a simple, but realistic treatment of initial 2p-2h excitations. Results: We show numbers and spectra of knock-out nucleons and show their sensitivity to the presence of 2p-2h initial excitations. We also discuss the influence of 2p-2h excitations on the neutrino energy reconstruction. Conclusions: 2p-2h excitations do lead to an increase in the number $n$ of knock-out nucleons for $n \ge 2$ while only the $n=1$ knock-out remains a clean signal of true QE scattering. The spectra of knock-out nucleons do also change, but their qualitative shape remains as before. In the energy reconstruction 2p-2h interactions lead to a downward shift of the reconstructed energy; this effect of 2p-2h excitations disappears at higher energies because the 2p-2h influence is spread out over a wider energy range.

Low-energy limit of the radiative dipole strength in nuclei

We explain the low-energy anomaly reported in several experimental studies of the radiative dipole strength functions in medium-mass nuclei. These strength functions at very low $\ensuremath{\gamma}$ energies correspond to the $\ensuremath{\gamma}$ transitions between very close nuclear excited states in the quasicontinuum and attract an increasing interest because of their substantial astrophysical impact. We show that the low-energy enhancement of the strength functions in highly excited compound nuclei is explained by nucleonic transitions from the thermally unblocked single-quasiparticle states to the single-(quasi)particle continuum. The case of radiative dipole strength functions at the nuclear excitation energies typical for the thermal neutron capture is illustrated for ${}^{94,96,98}$Mo and ${}^{116,122}$Sn in comparison to available data.

Many-body interactions of neutrinos with nuclei: Observables

Background: The total inclusive cross sections obtained for quasielastic (QE) scattering in the Mini Booster Neutrino Experiment (MiniBooNE) are significantly larger than those calculated by all models based on the impulse approximation and using the world average value for the axial mass of ${M}_{A}\ensuremath{\approx}1\phantom{\rule{0.28em}{0ex}}\mathrm{GeV}$. This discrepancy has led to various, quite different explanations in terms of increased axial masses, changes in the functional form of the axial form factor, increased vector strength in nuclei, and initial two-particle interactions. This is disconcerting since the neutrino energy reconstruction depends on the reaction mechanism.Purpose: We investigate whether exclusive observables, such as nucleon knockout, can be used to distinguish between the various proposed reaction mechanisms. We determine the influence of 2p-2h excitations on the neutrino energy reconstruction.Method: We extend the Giessen Boltzmann--Uehling--Uhlenbeck (GiBUU) model by explicitly incorporating initial 2p-2h excitations.Results: We calculate inclusive cross sections and numbers and spectra of knockout nucleons and show their sensitivity to the presence of 2p-2h initial excitations. We also discuss the influence of 2p-2h excitations on the neutrino energy reconstruction.Conclusions: Inclusive double-differential cross sections, depending only on muon variables, are fairly insensitive to the reaction mechanism. 2p-2h excitations lead to an increase in the number $n$ of knockout nucleons for $n\ensuremath{\geqslant}2$, while only the $n=1$ knockout remains a clean signal of true QE scattering. The spectra of knockout nucleons are also changed, but their shape is hardly affected. In the energy reconstruction, 2p-2h interactions as well as $\ensuremath{\Delta}$ excitations lead to a downward shift of the reconstructed energy; this effect of 2p-2h excitations disappears at higher energies because the 2p-2h influence is spread out over a wider energy range.

Pygmy dipole resonance in208Pb

Scattering of protons of several hundred MeV is a promising new spectroscopic tool for the study of electric dipole strength in nuclei. A case study of 208Pb shows that at very forward angles J^pi = 1- states are strongly populated via Coulomb excitation. A separation from nuclear excitation of other modes is achieved by a multipole decomposition analysis of the experimental cross sections based on theoretical angular distributions calculated within the quasiparticle-phonon model. The B(E1) transition strength distribution is extracted for excitation energies up to 9 MeV, i.e., in the region of the so-called pygmy dipole resonance (PDR). The Coulomb-nuclear interference shows sensitivity to the underlying structure of the E1 transitions, which allows for the first time an experimental extraction of the electromagnetic transition strength and the energy centroid of the PDR.

Dipole response of238U to polarized photons below the neutron separation energy

1) dipole strengths in nuclei[1]. Observation of dipole states are important because theycharacterize the various collective and single-particle nuclearexcitation modes, in particular, the scissors mode, the spin-flip mode, and the pygmy dipole resonance. These differentexcitation modes are prominent in various regions below ornear the neutron separation energy and represent importantnuclear structure phenomena. For

Isovector dipole strength in nuclei with extreme neutron excess

The $E1$ strength is systematically analyzed in very neutron-rich Sn nuclei, beyond $^{132}\mathrm{Sn}$ until $^{166}\mathrm{Sn}$, within the relativistic quasiparticle random phase approximation. The great neutron excess favors the appearance of a deformed ground state for $^{142\ensuremath{-}162}\mathrm{Sn}$. The evolution of the low-lying strength in deformed nuclei is determined by the interplay of two factors, isospin asymmetry and deformation: while greater neutron excess increases the total low-lying strength, deformation hinders and spreads it. Very neutron rich deformed nuclei may not be as good candidates as spherical nuclei like $^{132}\mathrm{Sn}$ for the experimental study of low-lying $E1$ strength.

Low-lyingE1strength in light drip-line nuclei

By adopting a finite square-well potential, the analytic expressions of $\mathit{dB}(E1)/{\mathit{dE}}_{x}$ for the cases of ${\ensuremath{\ell}}_{h}=0\ensuremath{\rightarrow}{\ensuremath{\ell}}_{c}=1,{\ensuremath{\ell}}_{h}=1\ensuremath{\rightarrow}{\ensuremath{\ell}}_{c}=0,{\ensuremath{\ell}}_{h}=1\ensuremath{\rightarrow}{\ensuremath{\ell}}_{c}=2$, and ${\ensuremath{\ell}}_{h}=2\ensuremath{\rightarrow}{\ensuremath{\ell}}_{c}=1$ are derived in the distorted wave approximation (DWA). From these analytic expressions it can be seen clearly that enhanced low-lying $B(E1)$ strengths in nuclei near drip-line mainly come from the orbits with small binding energy and small angular momentum. Comparing the results of analytic expressions with the experimental $\mathit{dB}(E1)/{\mathit{dE}}_{x}$ data, the spectroscopic factors of the $2{s}_{1/2}$ state in $^{11}\mathrm{Be}$ were deduced as 0.92, 0.87, and 0.83 for the well depths ${U}_{0}=50$ MeV, 40 MeV, and 33 MeV, respectively.

Direct reactions with exotic nuclei, nuclear structure and astrophysics

Intermediate energy Coulomb excitation and dissociation is a useful tool for nuclear structure and astrophysics studies. Low-lying strength in nuclei far from stability was discovered by this method. The effective range theory for low-lying strength in one-neutron halo nuclei is summarized and extended to two-neutron halo nuclei. This is of special interest in view of recent rather accurate experimental results on the low-lying electric dipole strength in 11Li. Another indirect approach to nuclear astrophysics is the Trojan-horse method. It is pointed out that it is a suitable tool to investigate subthreshold resonances.

GAMOW–TELLER SUM RULE IN RELATIVISTIC NUCLEAR MODELS

Relativistic corrections are investigated to the Gamow–Teller (GT) sum rule with respect to the difference between the β- and β+ transition strengths in nuclei. Since the sum rule requires the complete set of the nuclear states, the relativistic corrections come from the anti-nucleon degrees of freedom. In the relativistic mean field approximation, the total GT strengths carried by the nucleon sector is quenched by about 12% in nuclear matter, while by about 8% in finite nuclei, compared to the sum rule value. The coupling between the particle-hole states with the nucleon–antinucleon states is also discussed with the relativistic random phase approximation, where the divergence of the response function is renormalized with use of the counterterms in the Lagrangian. It is shown that the approximation to neglect the divergence, like the no-sea approximation extensively used so far, is unphysical, from the sum-rule point of view.

SATURATION PROPERTIES OF NUCLEAR MATTER AND CORRELATED NUCLEONS

A brief overview is given of the properties of spectral functions in finite nuclei as obtained from ( e,e ′ p ) experiments. Based on recent experimental data from this reaction it is argued that the empirical value of the saturation density of nuclear matter is dominated by short-range correlations. This observation and the observed fragmentation and depletion of the single-particle strength in nuclei provide the motivation for attempting a self-consistent description of the nucleon spectral functions with full inclusion of short-range and tensor correlations in nuclear matter. Results for these "second generation" spectral functions will be discussed with emphasis on the consequences for the saturation properties of nuclear matter. Arguments are presented to clarify the obscuring role of pionic long-range correlations in this long-standing problem.

Radiative strength functions for nuclei in which the number of protons is close to the magic number of Z=28

The distribution of the radiative strength in nuclei where the number of nucleons of one type is nearly magic (Z=28±1) and where there are a few valence nucleons of the other type is investigated. It is shown that the statistical approach that is based on Fermi liquid theory and which takes into account temperature and the shell structure of nuclei leads to good agreement with experimental data on radiative strength functions below the neutron binding energy in such nuclei. Only for the 59Co and 65Cu nuclei, which have the largest number of valence neutrons among the cobalt and copper isotopes being investigated, is the energy dependence of the radiative strength compatible with a Lorentz distribution as well.

From atomic helium to nuclear matter

Differences between the quasiparticle and the bare particle, as constituents of Fermi systems, mainly result from the effects of correlations. Comparative studies performed in liquid helium and indicating interesting similarities in the single particle properties of Bose and Fermi liquids will be discussed, also in connection with the theoretical and experimental quasihole strength in nuclei. A new Quantum Monte Carlo method for nuclear systems is also outlined.

The Giant Dipole Resonance in Ar-Isotopes in the Relativistic RPA

The isovector giant dipole resonance in Ar-isotopes is studied in the framework of the relativistic random phase approximation starting from effective Lagrangians originally pro­ posed for describing nuclear ground states. The calculations are done with the parameter set TMI which satisfactorily describes the ground states of stable and unstable nuclei up to the drip lines. It is found that the isovector dipole strength in nuclei near drip lines is split into two components: one peaks at the normal giant dipole energy, the other is located at low energy. The lower dipole state is due to the weakly bound neutron (or proton) excitation, which may cause large cross-sections in collisions with heavy nuclei by Coulomb excitation.

Enhancement of the isovectorM1strength in28Si due to meson exchange currents

Meson exchange currents (MEC's) can induce an enhancement of the $B(M1)$ strength in nuclei over the corresponding Gamow-Teller strength. Such an increase was observed in ${}^{28}$Si [C. L\"uttge et al., Phys. Rev. C 53, 127 (1996)], but the experimental ratio was much larger than shell model predictions using the unified $\mathrm{sd}$-shell interaction and corrections to the $g$ factors which incorporate MEC effects. It is pointed out that, when taking the Gamow-Teller strength from a reanalysis of the ${}^{28}$Si$(p,n)$ data as well as from a recent ${}^{28}{\mathrm{S}\mathrm{i}(}^{3}\mathrm{H}\mathrm{e},t)$ experiment, the derived ratio is now in good agreement with the shell model results. This finding provides strong support that the observed enhancement is due to meson exchange currents.

Localized 1ħω particle-hole strength in nuclei

A cross section enhancement, persisting to high momentum transfer, has been observed around 1HBAR omega in excitation energy in spectra from inelastic proton-, alpha- and electron scattering on Zr-90, Sn-116, Pt-196 and Pb-208. Data are presented for (p,p') at 201 MeV, (alpha,alpha') at 120 MeV and analyzed together with existing data obtained with 133.8 MeV polarized ((p) over right arrow,p') on Sn-116 and electron-scattering data on Sn-116 and Pt-196. Two different interpretations of the observed enhancement are discussed: that of the incoherent sum of all 1HBAR omega cross section and alternatively the sum over the isoscalar normal modes of all multipolarities.

Distribution of low lying quadrupole phonon strength in nuclei.

The distribution of quadrupole phonon strength to low-lying states in nuclei is examined. It is found that the ${2}_{1}^{+}$ and ${4}_{1}^{+}$ states of all nuclei from $Z=30 \mathrm{to} 100$ display almost perfect quadrupole phonon character even though they encompass widely ranging structures. The interacting boson approximation reproduces both the very small deviations from phonon purity and the distribution of those deviations as a function of mean field structure in a natural fashion. Simple physical mechanisms explain these results.

Gamow-Teller strength in nuclei with N=Z from 12C to 100Sn

Experimental and theoretical Gamow-Teller strength in N=Z nuclei from 12C to 100Sn are discussed. The effects of ground-state correlations for the total strength are calculated with full 0ħω 1p and 1d2s shell wavefunctions, and the relative importance of 0ħω and higher ħω correlations is pointed out. The GT strength in 16O which vanishes in the LS closed-shell limit is calculated in a 4ħω shell model basis. Unique features of the GT decay of 100Sn and neighboring nuclei are presented.

Spin isospin strength from heavy ions-stable and radioactive beams

Because heavy ion reactions have great promise for studying spin strength in nuclei, there has been an upsurge in experimental work. However, too little attention has been paid to verifying that these reactions provide a quantitative measure of spin strength. This paper reviews the work that has been done along these lines, to clarify what remains to be done. The first charge exchange experiments experiments with radioactive beams, done at MSU/NSCL, are also described briefly.