Isoscalar Monopole Resonance Research Articles

Description of the Proton-Decaying 0_{2}^{+} Resonance of the α Particle.

The recent precise experimental determination of the monopole transition form factor from the ground state of ^{4}He to its 0_{2}^{+} resonance via electron scattering has reinvigorated discussions about the nature of this first excited state of the α particle. The 0_{2}^{+} state has been traditionally interpreted in the literature as the isoscalar monopole resonance (breathing mode) or, alternatively, as a particle-hole shell-model excitation. To better understand the nature of this state, which lies only ∼410 keV above the proton emission threshold, we employ the coupled-channel representation of the no-core Gamow shell model. By considering the [^{3}H+p], [^{3}He+n], and [^{2}H+^{2}H] reaction channels, we explain the excitation energy and monopole form factor of the 0_{2}^{+} state. We argue that the continuum coupling strongly impacts the nature of this state, which carries characteristics of the proton decay threshold.

Revisiting the 4He(4He,4He)4He* inelastic scattering at the MAGNEX facility

The 4He(4He,4He)4He* inelastic scattering was investigated at the MAGNEX facility of INFN - LNS, aiming at shedding light on the characteristics of the isoscalar monopole resonance of 4He which lies at an energy slightly higher than the proton emission threshold and slightly lower than the neutron emission threshold. A complementary elastic scattering measurement was also performed to study the initial state interaction and set accurate coupled channel calculations. Here, the experimental setup, the data reduction and the theoretical interpretation strategy are briefly described.

Nuclear Equation of State in the Relativistic Point-Coupling Model Constrained by Excitations in Finite Nuclei

Nuclear equation of state is often described in the framework of energy density functional. However, the isovector channel in most functionals has been poorly constrained, mainly due to rather limited available experimental data to probe it. Only recently, the relativistic nuclear energy density functional with an effective point-coupling interaction was constrained by supplementing the ground-state properties of nuclei with the experimental data on dipole polarizability and isoscalar monopole resonance energy in 208Pb, resulting in DD-PCX parameterization. In this work, we pursue a complementary approach by introducing a family of 8 relativistic point-coupling functionals that reproduce the same nuclear ground-state properties, including binding energies and charge radii, but in addition have a constrained value of symmetry energy at saturation density in the range J = 29, 30, …, 36 MeV. In the next step, this family of functionals is employed in studies of excitation properties such as dipole polarizability and magnetic dipole transitions, and the respective experimental data are used to validate the optimal choice of functional as well as to assess reliable values of the symmetry energy and slope of the symmetry energy at saturation.

Nuclear multipole responses from chiral effective field theory interactions

We probe nuclear multipole resonances in the framework of the random-phase approximation by using the interaction obtained from the chiral effective field theory. The three-nucleon force is included in a form of the in-medium two-nucleon interaction which was derived from the chiral three-nucleon force. The isoscalar monopole, isoscalar dipole, isovector dipole and isoscalar quadrupole resonances of the closed-shell $^{56,68,78}$Ni have been investigated. The calculations reasonably reproduce the experimental multipole resonances of $^{56,68}$Ni, and well describe the pygmy dipole resonance and dipole polarizability measured in $^{68}$Ni. The multipole resonances of $^{78}$Ni, including pygmy dipole resonance and dipole polarizability, are predicted. The detailed effects of the tensor force and three-body force are analyzed by dissecting the chiral interaction. We find that in general the tensor force effect on electric giant resonances is not as significant as the effect from the three-body force, although the tensor force provides more than half of the binding energy. The effect from three-body force is strong in light nuclei. Particularly, three-body force is crucial for the formation of the pygmy resonance in calculations.

Chiral NNLOsat descriptions of nuclear multipole resonances within the random-phase approximation

We study nuclear multipole resonances in the framework of the random phase approximation using the chiral potential NNLO$_{\text{sat}}$. This potential includes two- and three-body terms that has been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main foci have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, $^4$He, $^{16,22,24}$O, and $^{40,48}$Ca. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential $V_{\text{low-}k}$, based on the N$^3$LO two-body potential by Entem and Machleidt [Phys. Rev. \textbf{C68}, 041001 (2011)]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLO$_{\text{sat}}$ can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the $V_{\text{low-}k}$ potential that simultaneously describe the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich $^{22,24}$O show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that $^{22}$O and $^{24}$O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.

Ab initio calculations for non-strange and strange few-baryon systems

Concerning the non-strange particle systems the low-energy excitation spectra of the three- and four-body helium isotopes are studied. Objects of the study are the astrophysical S-factor S12 of the radiative proton deuteron capture d(p, )3He and the width of the 4He isoscalar monopole resonance. Both observables are calculated using the Lorentz integral transform (LIT) method. The LIT equations are solved via expansions of the LIT states on a specifically modified hyperspherical harmonics (HH) basis. It is illustrated that at low energies such a modification allows to work with much higher LIT resolutions than with an unmodified HH basis. It is discussed that this opens up the possibility to determine astrophysical S-factors as well as the width of low-lying resonances with the LIT method. In the sector of strange baryon systems binding energies of the hypernucleus H are calculated using a nonsymmetrized HH basis. The results are compared with those calculated by various other groups with different methods. For all the considered non-strange and strange baryon systems it is shown that high-precision results are obtained.

Resolution of resonances with the Lorentz integral transform

The energy resolution of cross sections calculated with the Lorentz integral transform (LIT) method is investigated. It is shown that a crucial role is played by the density of LIT states obtained in the calculation. The situation is illustrated for the simple case of deuteron photodisintegration in unretarded dipole approximation. In a next step the 4 He isoscalar monopole resonance is considered. It is pointed out that in a specific energy interval the density of LIT states may depend on the A -body basis chosen for the solution of the LIT equation. Using a central NN potential and choosing a proper A -body basis set it is shown that the width of the 4 He isoscalar monopole resonance can be determined. A value of 180(70) keV is obtained, which is close to the experimental value of 270(50) keV.

Is the isoscalar monopole resonance of theα-particle a collective mode?

In this contribution we review and clarify the arguments which might allow the interpretation of the isoscalar monopole resonance of $^4$He as a collective breathing mode.

Energy resolution with the Lorentz integral transform

A brief outline of the Lorentz Integral Transform (LIT) method is given. The method is well established and allows to treat reactions into the many-body continuum with bound-state like techniques. The energy resolution that can be achieved is studied by means of a simple two-body reaction. From the discussion it will become clear that the LIT method is an approach with a controlled resolution and that there is no principle problem to even resolve narrow resonances in the many-body continuum. As an example the isoscalar monopole resonance of 4He is considered. The importance of the choice of a proper basis for the expansion of the LIT states is pointed out. Employing such a basis a width of 180(70) keV is found for the 4He isoscalar monopole resonance when using a simple central nucleon-nucleon potential model.

Isoscalar monopole resonance of the alpha particle: a prism to nuclear Hamiltonians.

We present an ab initio study of the isoscalar monopole excitations of (4)He using different realistic nuclear interactions, including modern effective field theory potentials. In particular we concentrate on the transition form factor F(M) to the narrow 0(+) resonance close to threshold. F(M) exhibits a strong potential model dependence, and can serve as a kind of prism to distinguish among different nuclear force models. Compared to the measurements obtained from inelastic electron scattering off ^{4}He, one finds that the state-of-the-art theoretical transition form factors are at variance with experimental data, especially in the case of effective field theory potentials. We discuss some possible reasons for such a discrepancy, which still remains a puzzle.

Microscopic study of the isoscalar giant resonances in 208Pb induced by inelastic α scattering

The energetic beam of (spin and isospin zero) α-particles remains a very efficient probe for the nuclear isoscalar giant resonances. In the present work, a microscopic folding model study of the isoscalar giant resonances in 208Pb induced by inelastic α + Pb 208 scattering at E lab = 240 and 386 MeV has been performed using the (complex) CDM3Y6 interaction and nuclear transition densities given by both the collective model and Random Phase Approximation (RPA) approach. The fractions of energy weighted sum rule around the main peaks of the isoscalar monopole, dipole and quadrupole giant resonances were probed in the Distorted Wave Born Approximation analysis of inelastic α + Pb 208 scattering using the double-folded form factors given by different choices of the nuclear transition densities. The energy distribution of the E0, E1 and E2 strengths given by the multipole decomposition analyses of the ( α , α ′ ) data under study are compared with those predicted by the RPA calculation.

Continuum random-phase approximation for relativistic point coupling models

Relativistic Continuum Random Phase Approximation (CRPA) is used to investigate collective excitation phenomena in several spherical nuclei along the periodic table. We start from relativistic mean field calculations based on a covariant density functional with density dependent zero range forces. From the same functional an effective interaction is obtained as the second derivative with respect to the density. This interaction is used in relativistic continuum-RPA calculations for the investigation of isoscalar monopole, isovector dipole and isoscalar quadrupole resonances of spherical nuclei. In particular we study the low-lying E1 strength in the vicinity of the neutron evaporation threshold. The properties of the resonances, such as centroid energies and strengths distributions are compared with results of discrete RPA calculations for the same model as well as with experimental data.

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the Random Phase Approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the Unitary Correlation Operator Method (UCOM), and (ii) relativistic RPA (RRPA) derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of an unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar monopole resonance (ISGMR) in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the Relativistic Quasiparticle RPA (RQRPA) based on Relativistic Hartree-Bogoliubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip-line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.

Compression mode resonances inZr90

The giant resonance region from $10\phantom{\rule{0.3em}{0ex}}\text{MeV}l{E}_{x}l55\phantom{\rule{0.3em}{0ex}}\text{MeV}$ in $^{90}\mathrm{Zr}$ has been studied with inelastic scattering of $240\phantom{\rule{0.3em}{0ex}}\text{MeV}$ $\ensuremath{\alpha}$ particles at small angles including $0\ifmmode^\circ\else\textdegree\fi{}$. The isoscalar monopole resonance was found to contain $100\ifmmode\pm\else\textpm\fi{}12%$ of the $E0$ energy weighted sum rule with a centroid of $(17.81+0.32\ensuremath{-}0.20)\phantom{\rule{0.3em}{0ex}}\text{MeV}$. Eighty one percent of the isoscalar $E1$ energy weighted sum rule was located in two peaks having ${E}_{x}=(17.1\ifmmode\pm\else\textpm\fi{}0.4)$ and $(26.7\ifmmode\pm\else\textpm\fi{}0.5)\phantom{\rule{0.3em}{0ex}}\text{MeV}$, $\ensuremath{\Gamma}=(5.4\ifmmode\pm\else\textpm\fi{}0.3)$ and $(8.8\ifmmode\pm\else\textpm\fi{}1.0)\phantom{\rule{0.3em}{0ex}}\text{MeV}$, and containing $13\ifmmode\pm\else\textpm\fi{}3%$ and $70\ifmmode\pm\else\textpm\fi{}10%$, respectively, of the $E1$ energy weighted sum rule.

Status of the nuclear matter equation of state as determined from compression modes

The nuclear matter (NM) equation of state (EOS) is a very important ingredient in the study of properties of nuclei, heavy-ion collisions, neutron stars and supernova. An accurate determination of the symmetric NM incompressibility coefficientKnm, is needed in order to determine the EOS around the saturation point. We review the current status ofKnm, as deduced from a comparison of experimental data on excitation cross sections of isoscalar compression modes with theoretical predictions of relativistic and non-relativistic models. We present our recent theoretical results and discuss the resolutions of the long standing discrepancies in the value ofKnm deduced from (i) data on isoscalar monopole and dipole resonances and (ii) relativistic and non-relativistic calculations.

Status of the nuclear matter equation of state as determined from compression modes

The nuclear matter (NM) equation of state (EOS) is a very important ingredient in the study of properties of nuclei, heavy-ion collisions, neutron stars and supernova. An accurate determination of the symmetric NM incompressibility coefficientKnm, is needed in order to determine the EOS around the saturation point. We review the current status ofKnm, as deduced from a comparison of experimental data on excitation cross sections of isoscalar compression modes with theoretical predictions of relativistic and non-relativistic models. We present our recent theoretical results and discuss the resolutions of the long standing discrepancies in the value ofKnm deduced from (i) data on isoscalar monopole and dipole resonances and (ii) relativistic and non-relativistic calculations.

Status of the nuclear matter equation of state as determined from compression modes

The nuclear matter (NM) equation of state (EOS) is a very important ingredient in the study of properties of nuclei, heavy-ion collisions, neutron stars and supernova. An accurate determination of the symmetric NM incompressibility coefficient K nm , is needed in order to determine the EOS around the saturation point. We review the current status of K nm , as deduced from a comparison of experimental data on excitation cross sections of isoscalar compression modes with theoretical predictions of relativistic and non-relativistic models. We present our recent theoretical results and discuss the resolutions of the long standing discrepancies in the value of K nm deduced from (i) data on isoscalar monopole and dipole resonances and (ii) relativistic and non-relativistic calculations.

Compression modes in nuclei: RPA and QRPA predictions with Skyrme interactions

Isoscalar monopole and dipole resonances in 90Zr, 116Sn, 144Sm, and 208Pb are studied within the framework of self-consistent HF-RPA or HF-BCS plus quasiparticle RPA. A comparison with recent experimental data obtained at Texas A&M University, as well as the problems related to the determination of the nuclear incompressibility K ∞, is discussed.

Relativistic approach to isoscalar giant resonances in208Pb

We calculate the longitudinal response of 208Pb using a relativistic random-phase approximation to three different parameterizations of the Walecka model with scalar self-interactions. From a nonspectral calculation of the response-that automatically includes the mixing between positive- and negative-energy states-we extract the distribution of strength for the isoscalar monopole, dipole, and high-energy octupole resonances. We employ a consistent formalism that uses the same interaction in the calculation of the ground state as in the calculation of the response. As a result, the conservation of the vector current is strictly maintained throughout the calculation. Further, at small momentum transfers the spurious dipole strength-associated with the uniform translation of the center-of-mass-gets shifted to zero excitation energy and is cleanly separated from the sole remaining physical fragment located at an excitation energy of about 24 MeV; no additional dipole strength is observed. The best description of the collective modes is obtained using a ``soft'' parameterization having a compression modulus of K=224 MeV.

Microscopic analysis of the breathing mode in 40Ca and 58Ni

Recent experimental studies of the giant electric resonance region in 58Ni and 40Ca with inelastically scattered α-particles of energy Eα= 240 MeV are analyzed within a microscopic nuclear structure model. The model includes the continuum RPA and more complex 1p1h⊗phonon configurations. By superimposing the contributions of different multipoles up to L = 4 we obtain good agreement with the newest (reanalyzed) data for the isoscalar monopole strength and for the total (α,α′) cross section in 58Ni. Agreement with experiment for the isoscalar monopole resonance in 40Ca is obtained too. We emphasize the necessity of using microscopic transition densities and discuss consequences for the analyses of such experiments in light and medium mass nuclei. It is shown that the gross structure of the isoscalar monopole resonance in 40Ca is caused by the 1p1h⊗phonon configurations.