Nucleon Separation Energies Research Articles

Overlap functions, spectroscopic factors, and asymptotic normalization coefficients generated by a shell-model source term

Overlap functions for one-nucleon removal are calculated as solutions of the inhomogeneous equation. The source term for this equation is generated by the $0\ensuremath{\hbar}\ensuremath{\omega}$ no-core shell-model wave functions and the effective nucleon-nucleon ($\mathit{NN}$) interactions that fit oscillator matrix elements derived from the $\mathit{NN}$ scattering data. For the lightest $A\ensuremath{\leqslant}4$ nuclei this method gives reasonable agreement with exact ab initio calculations. For $4lA\ensuremath{\leqslant}16$, this method gives a fair agreement between the calculated and measured asymptotic normalization coefficients. The spectroscopic factors obtained show systematic deviation from the corresponding shell-model values. This deviation correlates with nucleon separation energies and follows a similar trend seen in the reduction factor of the nucleon knockout cross sections. Comparison with the overlap functions and spectroscopic factors obtained in the variational Monte Carlo method is presented and discussed.

New Insight into the Observation of Spectroscopic Strength Reduction in Atomic Nuclei: Implication for the Physical Meaning of Spectroscopic Factors

Experimental studies of one-nucleon knockout from magic nuclei suggest that their nucleon orbits are not fully occupied. This conflicts a commonly accepted view of the shell closure associated with such nuclei. The conflict can be reconciled if the overlap between initial and final nuclear states in a knockout reaction are calculated by a nonstandard method. The method employs an inhomogeneous equation based on correlation-dependent effective nucleon-nucleon interactions and allows the simplest wave functions, in which all nucleons occupy only the lowest nuclear orbits, to be used. The method also reproduces the recently established relation between reduction of spectroscopic strength, observed in knockout reactions on other nuclei, and nucleon binding energies. The implication of the inhomogeneous equation method for the physical meaning of spectroscopic factors is discussed.

Nuclear masses near the proton drip-line and their impact on nucleosynthesis in explosive stars

The interplay of the fundamental forces (here mainly the strong force and electromagnetic force) holds nucleons together to form atomic nuclei. However, in nature only less than ten percent of the total number of nuclei is stable. The majority of nuclei are unstable; that is, after having lived for a certain time, they change into the daughter nuclei by radioactive decay. The familiar decay types that can be found in most parts of the chart of nuclide are α-decay and β-decay. There are other important processes in which unstable nuclei can change into other ones. These occur, for example, in very neutronrich or proton-rich regions of the chart of nuclide. There are boundaries called drip-lines, which are the lines on the Z (proton)-N (neutron) plane where the nucleon separation energy is zero. The nuclear binding becomes weaker and weaker when moving from the stable region towards the drip-lines, and eventually no nucleus can exist beyond the drip-lines. Taking the proton-rich region as an example, near the proton drip-line, protons are only weakly bound and a proton radioactivity can occur. Also because of the small binding, nuclei near the proton drip-line may capture additional protons and become new, heavier nuclides if the capture conditions are present. Detailed knowledge on the nucleon-capture processes lies at the heart of the understanding of nucleosynthesis in the Universe——a very fundamental but unanswered question about how the heavy elements (i.e. those heavier than iron) are created. In order for nuclei to capture protons, a high temperature environment (usually above 1×10 9 K) is needed so that they can overcome the large coulomb barrier for charged particle reactions. A hydrogen rich

PYGMY DIPOLE RESONANCES

Electric dipole strength below the particle emission threshold both in stable nuclei and short-lived isotopes has received increasing interest due to its astrophysical impact. In analogy to the giant dipole resonance, this strength is commonly referred to as pygmy resonance. Coulomb dissociation of neutron-rich unstable isotopes and nuclear resonance fluorescence photon scattering have begun to provide systematic data on electric dipole strength in various isotope chains. We review the present state of the art of theoretical approaches and point out some open problems. We emphasize the necessity of a simultaneous theoretical treatment of the nucleon separation energies and the energetically low-lying dipole strength because the presently available data do not exclude a non-collective nature of the pygmy strength.

Systematics of the (p, n) excitation functions belonged to several isotopes at energies

Excitation functions of proton induced charge exchange reaction on nuclei between A = 11 and 238 are studied. All the studied excitation functions of (p, n) reaction show systematic variation with atomic mass in connection with nucleon binding energy. Islands of higher reaction yield appeared to be for nuclei with mass number A = 49, 72, 89, 109, and 139, and proton energy range from 9 to 12 MeV. The more probable occurrence of proton induced charge exchange reaction in these regions are attributed to its extra binding energy per nucleon than other nuclei. The larger contribution of pre-equilibrium processes on the neutron emission appeared on the linearity of the log( σ)–log( E p ) in some energy ranges. The slopes of these linear segments may be related to the excitons configuration in which the neutron is emitted by.

Investigation on phase and shape transitions in the hot rotating nucleus 154Dy

A statistical theory for hot rotating nuclei incorporating deformation, collective and non-collective rotational degrees of freedom, shell effects and pairing correlations is used to investigate the occurrence of phase and shape transitions in the hot rotating deformed nucleus 154Dy . The interplay of various degrees of freedom and their influence on the behavior of nuclei formed as fused compounds in heavy-ion reactions are studied. A phase transition from the superfluid to normal state in the nucleus with increasing temperature and angular momentum is observed. The effect of pairing on the level density parameter and nucleon separation energy has been analyzed and is found to be substantial. The neutron and proton separation energies extracted as a function of the angular momentum and temperature is found to decrease sharply for particular angular momentum states of the nucleus due to shape transitions from prolate collective to oblate non-collective at higher temperatures.

Shell closures in the N and Z=40–60 region for neutron and proton-rich nuclei

Abstract A systematic study of shell closures around N and Z = 40 – 60 through beta decay Q-values, one nucleon separation energies and excited states is presented for different isospin chains. Shell closure at N = 40 is found to be absent in neutron-rich nuclei (contrary to some existing discussions) but is indicated in nuclei with T z ⩽ 1 within errors. The persistence of the N and Z = 50 shell closure is observed, together with evidence of sub-shell closure at N = 56 in neutron-rich nuclei. The sub-shell closure at Z = 40 , that exists for neutron-rich nuclei, is found to disappear for T z = 2 .

Photonuclear data and modern physics of giant resonances

The results of the development (“renaissance”) of giant-resonance physics are briefly discussed from the point of view of their application to creating a photonuclear database. It is indicated that part of the recommendations from corresponding libraries of data are not at the level of the present-day status of giant-resonance physics. A Lorentzian parametrization of the most reliable experimental data on isovector M1 resonances is constructed for seven spherical nuclei, and it is shown that the widths of M1 resonances are severalfold, sometimes an order of magnitude, smaller than the value of Γ0 = 4 MeV, which was recommended for all nuclei. The need for microscopically taking into account configurations more complex than those that are included within the standard random-phase approximation or within the quasiparticle random-phase approximation is emphasized. To be more precise, it is necessary to take into account coupling to phonons, since this changes the temperature dependence of the resonance width in relation to that which was used earlier and since, without this, one cannot explain the properties of pygmy dipole resonances in the region of the nucleon binding energy. Our calculations of the average energies of the pygmy dipole resonances in the Ca and Sn isotopes within the microscopic extended theory of finite Fermi systems reveal that the inclusion of coupling to phonons reduces these energies considerably toward the improvement of agreement with experimental data. The idea of creating a library of photonuclear data for unstable nuclei, including fission fragments, on the basis of the extended theory of finite Fermi systems is discussed in connection with the fact that information necessary for fitting the parameters of phenomenological theories is absent or insufficient for such nuclei.

Towards an optimum design of a P-MOS radiation detector for use in high-energy medical photon beams and neutron facilities: analysis of activation materials

The behaviour of packaged and unpackaged ESAPMOS4 RadFET radiation detectors (NMRC Cork, Ireland) was investigated when used in the mixed photon and neutron environment of a medical linear accelerator operating above the nucleon separation energy and in a 14 MeV neutron field provided by a D-T generator. Within the uncertainty of the experimental set-up (4% at 95% confidence level) the unpackaged device was found to have essentially zero activation dose-burden whereas the packaged device exhibits a considerable degree of post irradiation absorbed dose due to deactivation radiation.

NEW PROTON AND NEUTRON MAGIC NUMBERS IN NEUTRON-RICH NUCLEI

It is now known that in neutron-rich nuclei, old magic numbers disappear and new ones appear. Single nucleon and double nucleon separation energies are plotted here in all possible manner. Using this data it is shown here that nuclei with pair of proton number Z and neutron number N(Z,N): (6, 12), (8, 16), (10, 20), (11, 22) and (12, 24) exhibit exceptional stability or magicity. As such these magic numbers appear in pairs. This correlation is shown here to be indicative of predominance of tritons in the ground state of these neutron-rich nuclei. Thus [Formula: see text] has the structure of 10 [Formula: see text] in the ground state. It is shown here that this is due to fundamental symmetry arguments based on a new symmetry group [Formula: see text] nusospin.

Electromagnetic strength of neutron and proton single-particle halo nuclei

Electromagnetic strength functions of halo nuclei exhibit universal features that can be described in terms of characteristic scale parameters. For a nucleus with nucleon + core structure the reduced transition probability, as determined, e.g., by Coulomb dissociation experiments, shows a typical shape that depends on the nucleon separation energy and the orbital angular momenta in the initial and final states. The sensitivity to the final-state interaction (FSI) between the nucleon and the core can be studied systematically by varying the strength of the interaction in the continuum. In the case of neutron + core nuclei analytical results for the reduced transition probabilities are obtained by introducing the effective-range expansion. The scaling with the relevant parameters is found explicitly. General trends are observed by studying several examples of neutron + core and proton + core nuclei in a single-particle model assuming Woods–Saxon potentials. Many important features of the neutron halo case can be obtained from a square-well model. Rather simple analytical formulas are found. The nucleon–core interaction in the continuum affects the determination of astrophysical S factors at zero energy in the method of asymptotic normalisation coefficients (ANC). It is also relevant for the extrapolation of radiative capture cross sections to low energies.

Improved implementation of the transfer-to-the-continuum method for single-neutron knockout reactions and the validity of standard approximations

Approximations made in implementing the transfer-to-the-continuum model for single-nucleon knockout reactions on light target nuclei are investigated using more complete numerical calculations. The reliability of different proposed approximation schemes and their predicted cross sections are discussed. The results of the model calculations that use realistic descriptions of the distorting interactions entering the theory are also compared with available experimental data for reactions induced by $^{15}\mathrm{C}$ and $^{34}\mathrm{Si}$ secondary beams. These transitions, with different neutron orbital angular momenta, also have significantly different values of the neutron separation energy. The different approximation schemes are shown to agree most closely for the weakly bound and spatially extended, $l=0,^{15}\mathrm{C}$ ground state transition. For an $l=2$ transition in $^{34}\mathrm{Si}$, the approximation schemes are shown to be dependent on the nucleon separation energy. In all cases comparisons of even the most accurate implementation of the theory with the experimental data reveals deviations in both the magnitudes of the predicted integrated cross sections and their momentum distributions. Furthermore, the use of the different approximation schemes also produce quite significant effects on the shapes of the predicted momentum distributions and the integrated partial cross sections.

Equation of State of Nuclear Matter in Chiral σ-ω Model**The project supported by National Natural Science Foundation of China under Grant Nos. 10275099, 10347124, and 10175096, and the Natural Science Foundation of Guangdong Province of China under Grant No. 001182

The equation of state of nuclear matter is studied in the 1-loop approximation of chiral linear σ-ω model. By introducing the density-dependent coupling constants, the problem of tachyon pole in the chiral σ-ω model is resolved. The 1-loop contributions of σ and π mesons to the nucleon's binding energy are included, while the empirical properties of nuclear matter such as saturation density, binding energy, and incompressibility are well reproduced.

Collective excitations close to the particle threshold

High resolution photon scattering experiments with very high sensitivity have been performed at the superconducting Darmstadt electron accelerator S-DALINAC. The energy range from about 3 MeV up to the nucleon separation energy has been investigated. The electric dipole strength distributions measured in this way show a concentration of strength in the 1ħ region exhausting up to one percent of the isovector Energy Weighted Sum Rule (EWSR) for various nuclei. A systematic study on the N=82 isotonic chain seems to hint to a correlation of the summed strength with the nucleon skin.

Collective excitations close to the particle threshold

High resolution photon scattering experiments with very high sensitivity have been performed at the superconducting Darmstadt electron accelerator S-DALINAC. The energy range from about 3 MeV up to the nucleon separation energy has been investigated. The electric dipole strength distributions measured in this way show a concentration of strength in the 1ħ region exhausting up to one percent of the isovector Energy Weighted Sum Rule (EWSR) for various nuclei. A systematic study on the N=82 isotonic chain seems to hint to a correlation of the summed strength with the nucleon skin.

Green’s function method in the problem of complex configurations in fermi systems with pairing

The Green’s function method is used to derive general equations for describing effects of pairing in Fermi systems where there are two types of interaction, two-particle and quasiparticle-phonon interaction. These equations generalize Bardeen-Cooper-Schrieffertheory to the case of complex configurations involving “strong” phonons. In the approximation of weak coupling to phonons, realistic equations that make it possible to describe excited states of nonmagic even-even nuclei with allowance for a single-particle continuum and complex configurations of the two quasiparticles ⊗ phonon type are formulated for the first time. These equations are solved for an isovector E 1 resonance in the stable isotope 120 Sn and in the unstable isotopes 104,132Sn. It is shown that complex configurations must be taken into account in order to describe E1 excitations—in particular, in a broad energy region around the nucleon binding energy.

Relativistic mean field calculation for odd mass nuclei inA∼60–70region

Relativistic mean field calculation has been performed for odd mass nuclei with $A\ensuremath{\sim}60--70$. The mean field is assumed to be axially symmetric and time-reversal symmetric. Blocked BCS method is used to restore time-reversal symmetry. The total binding energy and the last nucleon binding energy are reproduced with reasonable accuracy. The static quadrupole moments of different nuclei in their ground states are calculated and compared with experiment. In many nuclei, a number of solutions with different shapes but comparable energy values are obtained by blocking different single particle levels. In a few nuclei, the ground state spin is not reproduced.

On Consistent Description of Nuclear Level Density

The back–shifted Fermi gas (BSFG) model has been used for description of the nuclear level density at excitation energies up to the nucleon binding energy by fitting the latest experimental low–lying discrete levels and average s–wave nucleon resonance spacings D0. The analysis of the ratio of the proton and neutron resonance spacings corresponding to the same compound nucleus has led to the ratio IIr=(0.75±0.06) of the effective moment of inertia of the nucleus to the rigid-body value Ir for the nucleus 51V. The energy-dependent level density parameter and the method proposed by Koning and Chadwick for choosing the appropriate shell correction energy have been adopted for energies above the nucleon binding energy. Finally, a consistent description of all experimental data related to the nuclear level density, i.e. the low–lying discrete levels, the nucleon–resonance data, and the level density data above the nucleon binding energy, has been obtained for nuclei within A–ranges 24–41, 55–70, and 104–114.

The cluster–core model for the halo structure of light nuclei at the drip lines

Nuclei at both the neutron- and proton-drip lines are studied. In the cluster–core model, the halo structure of all the observed and proposed cases of neutron- or proton-halos is investigated in terms of simple potential energy surfaces calculated as the sum of binding energies, Coulomb repulsion, nuclear proximity attraction and the centrifugal potential for all the possible cluster+core configurations of a nucleus. The clusters of neutrons and protons are taken to be unbound, with additional Coulomb energy added for proton-clusters. The model predictions agree with the available experimental studies but show some differences with the nucleon separation energy hypothesis, particularly for proton-halo nuclei. Of particular interest are the halo structures of 11N and 20Mg. The calculated potential energy surfaces are also useful to identify the new magic numbers and molecular structures in exotic nuclei. In particular, N = 6 is a possible new magic number for very neutron-deficient nuclei, but N = 2, Z = 2 and Z = 8 seem to remain magic even for such nuclei, near the drip line.

Modification of Shell Structure for Unstable Nuclei

Studies of unstable nuclei have revealed that nuclear orbitals change their conventional ordering in regions far from stability. This is a contribution of several effects. Primarily it is an outcome of the small nucleon separation energy and a more diffused nucleon binding potential. This apart, changes of spin-orbit and pairing interactions may also be responsible for orbital re-orderings. The spin-isospin part of the nucleon-nucleon interaction has also been found to be important. The re-ordering of orbitals may lead to changes of shell closures, and appearance of new nucleon magic numbers.