Compression modes in nuclei: microscopic models with Skyrme interactions

The isoscalar giant monopole resonances (ISGMR) and giant dipole resonances (ISGDR) in medium-heavy nuclei are investigated in the framework of HF+RPA and HF-BCS+QRPA with Skyrme effective interactions. It is found that pairing has little effect on these modes. It is also found that the coupling of the RPA states to 2p-2h configurations results in about (or less than) 1 MeV shifts of the resonance energies and at the same time gives the correct total widths. For the ISGMR, comparison with recent data leads to a value of nuclear matter compression modulus close to 215 MeV. However, a discrepancy between calculated and measured energies of the ISGDR in $^{208}$Pb is found and remains an open problem.Comment: To appear in: ``RIKEN Symposium and Workshop on Selected Topics in Nuclear Collective Excitations'', proceedings of the meeting, RIKEN, Wako city (Japan), March 20--24, 199

Neutrino Capture Cross Sections for Ar-40 and beta-decay of Ti-40

Shell-model calculations of solar neutrino absorption cross sections for $^{40}$Ar, the proposed component of the ICARUS detector, are presented. It is found that low-lying Gamow-Teller transitions lead to a significant enhancement of the absorption rate over that expected from the Fermi transition between the isobaric analog states, leading to an overall absorption rate of 6.7 SNU. We also note that the pertinent Gamow-Teller transitions in ^{\sss 40}Ar are experimentally accessible from the $\beta$-decay of the mirror nucleus ^{\sss 40}Ti. Predictions for the branching ratios to states in ^{\sss 40}Sc are presented, and the theoretical halflife of 53~ms is found to be in good agreement with the experimental value of $56^{+18}_{-12}$~ms.Comment: 12 pages including references and table. NTGMI-94-

Elastic response of the atomic nucleus in gauge space:Giant Pairing Vibrations

Due to quantal fluctuations, the ground state of a closed shell system $A_{0}$ can become virtually excited in a state made out of the ground state of the neighbour nucleus $\vert gs(A_0+2) \rangle$ ($\vert gs(A_0-2) \rangle$) and of two uncorrelated holes (particles) below (above) the Fermi surface. These $J^{\pi} = 0^{+}$ pairing vibrational states have been extensively studied with two-nucleon transfer reactions. Away from closed shells, these modes eventually condense, leading to nuclear superfluidity and thus to pairing rotational bands with excitation energies much smaller than $\hbar\omega_{0}$, the energy separation between major shells. Pairing vibrations are the plastic response of the nucleus in gauge space, in a similar way in which low-lying quadrupole vibrations, i.e. surface vibrations with energies much smaller than $\hbar\omega_{0}$ whose eventual condensation leads to quadrupole deformed nuclei, provide an example of the plastic nuclear response in 3D space. While much is known, in particular concerning its damping, regarding the counterpart of quadrupole plastic modes, i.e. regarding the giant quadrupole resonances (GQR), $J^{\pi} = 2^{+}$ elastic response of the nucleus with energies of the order of $\hbar\omega_{0}$, little is known regarding this subject concerning pairing modes (giant pairing vibrations, GPV). Consequently, the recently reported observation of L = 0 resonances, populated in the reactions 12C(18O,16O)14C and 13C(18O,16O)15C and lying at an excitation energy of the order of $\hbar\omega_{0}$, likely constitutes the starting point of a new field of research, that of the study of the elastic response of nuclei in gauge space. Not only that, but also the fact that the GPV have likely been serendipitously observed in these light nuclei when it has failed to show up in more propitious nuclei like Pb, provides unexpected and fundamental insight into the relation existing between basic mechanisms --Landau, doorway, compound damping-- through which giant resonances acquire a finite lifetime, let alone the radical difference regarding these phenomena displayed by correlated (ph) and (pp) modes

Challenges in the description of the atomic nucleus: Unification and interdisciplinarity

Nuclear physics, in general, and theoretical nuclear physics, in particular, have provided the physics community at large, among other things, with the paradigm of spontaneous symmetry breaking phenomena in finite many-body systems. The study of the associated mechanisms of symmetry restoration has shed light on the microscopic structure of the corresponding condensates, in particular on the superfluid phase, allowing to study Cooper pair tunnelling into superfluid nuclei (related to the Josephson effect), in terms of individual quantum states and reaching, in doing so, a new milestone: that of unifying structure and reactions, these last processes being found at the basis of the formulation of quantum mechanics (probability interpretation, Born). In the process, nuclear physicists have extended the validity of BCS theory of superconductivity to the single Cooper pair situation, let alone discovering unexpected mechanism to break gauge invariance. The insight obtained from pair transfer research is likely to have important consequences in the study of double charge exchange processes, and thus in the determination of the nuclear matrix element associated with neutrinoless double beta decay, eventually providing an important test of the Standard Model. Time, thus, seems ripe for nuclear theorists to take centre stage, backed by a wealth of experimental information and by their interdisciplinary capacity to connect basic physical concepts across the borders. With the help of these elements they can aim at fully revealing the many facets of their femtometer many-body system, from vacuum zero point fluctuations to new exotic modes of nuclear excitations and of their interweaving, resulting in powerful effective field theories. Unless. Unless they are not able to free themselves from words like ab initio or fundamental, and to adapt a relax attitude concerning Skyrme, tensor, etc., forces, as well as regarding the quest for “the” Hamiltonian

Pairing Matrix Elements and Pairing Gaps with Bare, Effective and Induced Interactions

The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential $v_{low-k}$ is studied in the semiclassical approximation for the case of a typical finite, superfluid nucleus ($^{120}$Sn). It is found that the matrix elements of $v_{low-k}$ follow closely those of $v_{Gogny}$ on a wide range of energy values around the Fermi energy $e_F$, those associated with $v_{low-k}$ being less attractive. This result explains the fact that around $e_F$ the pairing gap $\Delta_{Gogny}$ associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective $k$-mass $m_k\approx 0.7 m$) is a factor of about 2 larger than $\Delta_{low-k}$,being in agreement with $\Delta_{exp}$= 1.4 MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction $v_{ind}$ peaked at $e_F$. The interaction $(v_{low-k}+ v_{ind})Z_{\omega}$ arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion ($\omega-$mass and quasiparticle strength $Z_{\omega}$) due to the particle-vibration coupling leads to a value of the pairing gap at the Fermi energy $\Delta_{ren}$ which accounts for the experimental value

Many-body effects in nuclear structure

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (120Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v14) in a Hartree-Fock basis (with effective k-mass m_k eqult to 0.7 m), within the framework of the BCS approximation including scattering states up to 800 MeV above the Fermi energy to achieve convergence. The resulting gap accounts for about half of the experimental gap. We find that a consistent description of the low-energy nuclear spectrum requires, aside from the bare nucleon-nucleon interaction, not only the dressing of single-particle motion through the coupling to the nuclear surface, to give the right density of levels close to the Fermi energy (and thus an effective mass m* approximately equal to m), but also the renormalization of collective vibrational modes through vertex and self-energy processes, processes which are also found to play an essential role in the pairing channel, leading to a long range, state dependent component of the pairing interaction. The combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time reversal states close to the Fermi energy accounts for the experimental gap.Comment: 5 pages, 4 figures; author list correcte