Calculated properties of superheavy nuclei

Ground-state properties of the heaviest nuclei are analyzed within a macroscopic-microscopic approach. The main attention is paid to such properties as deformation, deformation energy, energy of the first rotational state 2⁺ of a nucleus, and the branching ratio of α decay to this 2⁺ state with respect to the decay to the ground state 0⁺. The analysis concerns the problem of experimental confirmation of theoretically predicted deformed shapes of superheavy nuclei situated in the region around the nucleus ²⁷⁰Hs. A large region of even-even nuclei with proton, Z=82–128, and neutron, N=126–190, numbers is considered.     

Formation of 24Mg* in the spallation of 28Si nuclei by 1-GeV protons

The ²⁸Si(p, p′γ₀ X)²⁴Mg reaction has been studied at the ITEP accelerator by the hadron-gamma coincidence method for a proton energy of 1 GeV. Two reaction products are detected: a 1368.6-keV γ-ray photon accompanying the transition of the ²⁴Mg* nucleus from the first excited state to the ground state and a proton p′ whose momentum is measured in a magnetic spectrometer. The measured distribution in the energy lost by the proton in interaction is attributed to five processes: the direct knockout of a nuclear α cluster, the knockout of four nucleons with a total charge number of 2, the formation of the _ΔSi isobaric nucleus, the formation of the Δ isobar in the interaction of the incident proton with a nuclear nucleon, and the production of a π meson, which is at rest in the nuclear reference frame. The last process likely corresponds to the reaction of the formation of a deeply bound pion state in the ²⁸P nucleus. Such states were previously observed only on heavy nuclei. The cross sections for the listed processes have been estimated.     

Electromagnetic energies of nuclei and the nuclear compton amplitude

The electromagnetic energy of a nucleus is derived in perturbation theory, which relates this quantity to the amplitude for the forward scattering of virtual photons on a nucleus (nuclear Compton amplitude). Using the gauge invariance of this amplitude, the energy is separated into Coulomb and transverse components. Our formalism, although basically nonrelativistic, admits corrections of order ($\text{v}\text{c}$)² to the nuclear charge operator. The energy is further separated into one-body terms, related to the n-p mass difference, and two-body terms which lead to the Breit interaction and the nuclear Lamb shift. These results are then related to electron scattering sum rules in the manner of Cottingham. Mesonic contributions to the electromagnetic energy are also discussed.     

Initial population ofμ −,π −,K − after radiative atomic recombination

We calculate the radiative atomic recombination ofμ ^?,π ^?,K ^? with a nucleus. In the initial state the negative particle moves in a Coulomb field, in the continuous spectrum, with positive energy and is captured into the bound orbit (n,l) of negative energy. We consider the exotic atom as a hydrogenic atom. The analytical expression of the recombination cross section, together with a “low energy” approximation, is derived. We obtain information on the atomic initial population: the results presented here show that the Bohr statistical distribution, used in the case of neutral atoms, is not correct in this case.     

Use of (<Superscript>3</Superscript>He, <Emphasis Type="Italic">t</Emphasis>) charge-exchange reactions in determining radii of excited states of nuclei

A method for determining the radii of excited states of nuclei by means of (³He, t) charge-exchange reactions was proposed. Two versions of a comparison of differential cross sections for (³He, t) reactions were considered. The first relies on a comparison with cross sections for inelastic-scattering processes leading to the formation of isobaric analog states, while the second involves (³He, t) reactions leading to the production of the ground state. The two versions in question yield similar results and make it possible to determine the radius of the first excited state of the ¹³N nucleus. This state has the excitation energy of E* = 2.37 MeV, lying above the proton-emission threshold. The resulting radius proved to be enhanced in relation to the ground state and is close to the radius of the 3.09-MeV isobaric analog state of the ¹³С nucleus, which has a neutron halo. This permitted drawing the conclusion that the ¹³N nucleus in the 2.37-MeV state has a proton halo. The possibility of revealing a proton halo in other states of light nuclei is considered.     

Trajectory of virtual, bound and resonant Efimov states

The pole trajectory of Efimov states for a three-body ααβ system with αα unbound and αβ bound is calculated using a zero-range Dirac-δ potential. It is shown that a three-body bound state turns into a virtual one by increasing the αβ binding energy. This result is consistent with previous results for three equal mass particles. The present approach considers the n-n-¹⁸C halo nucleus. However, the results have good perspective to be tested and applied in ultracold atomic systems, where one can realize such three-body configuration with tunable two-body interaction.     

Proton halo in the <Superscript>13</Superscript>N nucleus

We demonstrate that the radii of excited nuclear states can be estimated using the (³He, t) charge-exchange reaction and relying on the modified diffraction model. The radius of the N excited state with an excitation energy of E*=2.73 MeV, which lies in a continuous spectrum, is determined. The radius of this state proves to be close to that of the mirror 3.09-MeV state of the ¹³С nucleus, which possesses a neutron halo but lies in a discrete spectrum. Thereby, we demonstrate that the 2.37-MeV state of the ¹³N nucleus has a proton halo. The analysis is based on published measurements of differential cross sections for relevant reactions.     

Resonance internal conversion in hydrogen-like ions

The resonance internal conversion effect in hydrogen-like ions is considered. For the M1 transition with an energy of 70.6 keV in ¹⁷¹Yb, the lifetime of this nucleus in the excited state decreases by five orders of magnitude as a result of deexcitation via a new channel—the resonance conversion—provided that the nuclear transition energy is equal to the energy of transition of a single 1s electron to a higher ns state. Observation of the resonance conversion in hydrogen-like ions is a powerful method for investigating their nuclear structure.     

Investigation of the mechanism of the reaction 10B(d, pγ)11B at E d = 15.3 MeV by the method of angular pγ correlations

The results are presented that were obtained by measuring the differential cross sections for the reaction ¹⁰B(d, p)¹¹B occurring at E _d = 15.3 MeV and leading to the production of a ¹¹B nucleus in the ground state (3/2^?) and in the lowest two excited states (the 1/2^? state at 2.125 MeV and the 5/2^? state at 4.445 MeV). The energy dependence of the differential cross section for this reaction was measured for several proton emission angles in the energy range E _d = 12–15.3 MeV. The double-differential cross sections for the reaction ¹⁰B(d, pγ)¹¹B were measured for the 5/2^? state of the ¹¹B nucleus at 4.445 MeV, and the angular dependences of the even spin-tensor components of the density matrix were reconstructed on the basis of these data. The angular dependences of the populations of magnetic sublevels are also given. The experimental results in question are compared with their theoretical counterparts obtained under the assumption of various reaction mechanisms (neutron stripping, heavy-particle stripping, and a two-step mechanism that takes into account the delay of interaction). On the basis of this comparison, the deformation parameters of the boron nuclei were found to be β ₂(¹⁰B) = ?0.55 and β ₂(¹¹B) = 0.4.     

The first order of the hyperspherical harmonic expansion method

The hyperspherical harmonic expansion method is studied in this work. Our attention is focused on the properties of the L_m-approximation in which only the hyperspherical harmonics of minimal order are taken into account. Exact solutions of the Schrödinger equation for a few simple hyperspherical potentials are given. Recipes for constructing antisymmetric hyperspherical harmonics for fermions are investigated, and various procedures to derive the effective potential in the L_m-approximation are discussed. The method is applied to the calculation of ground state and hyperradial excited states (which are identified as the breathing modes) of doubly-magic nuclei. Finally, the energy per particle is derived in the L_m-approximation with Skyrme like forces for an infinitely heavy self-conjugate nucleus.     

Shadowing,dipions and the EMC effect

The EMC effect is thought to be a compound phenomenon that appears when nucleons are bound in a nucleus. The shadowing effect shows up in a very low-x range. It is possible that in low- and medium-x ranges there exist weak-binding regions caused by the nucleon distortion in the nucleus as well as by exchange pions among the nucleons and other pions in weak-binding regions. Both these types of pions will be in the dipion state because of the Coulomb field. The dipion effect contributes to the structure function of the nucleus. Nuclear binding energy and Fermi motion in medium- and higher-x ranges cause a shift of the ratio of the nucleus structure function to the deuteron one. Calculations show that better agreement with recent data is obtained if the above three effects are mixed.     

Potential cluster approach to the description of the 7Li + γ ai p6He reactions

Angular distributions for the ⁶He(p, γ_{0 + 1})⁷Li process at the energy E _γ = 40 MeV are calculated within the potential cluster approach. It is shown that the observed cross section is well reproduced when E1 and E2 transitions are taken into account; in this case, unlike the case in the RGM calculations, the dominating mechanism is direct capture to the ground state of the ⁷Li nucleus. Total cross sections for direct photodisintegration ⁷Li (γ, p₀)⁶He in the energy interval E _γ = 22–30 MeV are calculated.     

Level density and collective enhancement factor of a compound nucleus in non-adiabatic approach

In this paper a simple statistical formalism that takes into account the diabatic motion of a compound system to calculate total level density is given. The diabatic motion is introduced by coupling the adiabatic collective motion to an environment consisting of intrinsic degrees of freedom. The collective enhancement of level density is studied. It has anadiabatical coefficient that depends only on the excitation energy and adynamical one that depends on the excitation energy and the coupling between intrinsic and collective modes. Qualitatively, the coefficients of the vibrational enhancement factor forA=240 have been studied. The coupling is understood as the initial effect of the oscillatory motion of the mass asymmetry of fragments on the nucleonic motion. The damping effect of the vibrational motion is taken into account considering the collective motion of the fragments as a zero-sound wave propagating in the Fermiliquid. The intrinsic state in the framework of the Fermi Gas Model (FGM) is described. The Pashkevich’s parametrization is used to describe the binary decay of the compound nucleus.     

Hyperfine structure of the energy levels of the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript> state of the Li-, B-, and N-like <Stack><Subscript>83</Subscript><Superscript>209</Superscript></Stack>Bi ions

The lowest order corrections, considering the electron-electron interaction, to the hyperfine structure of the energy levels of the Li-, B-, and N-like ₈₃ ²⁰⁹ BI ions in the 2p _3/2 state are calculated. The contributions of the magnetic dipole moment, electric quadrupole moment, and magnetic octupole moment are taken into account. The dynamic proton model is used, in which an electron interacts with a valence proton of a nucleus via photon exchange. In this model, the distribution of the electric and magnetic moments in a nucleus is taken into account automatically.     

The decay of93g Ru,93m Ru,91g Mo,91m Mo,91g Tc and91m Tc

Decay studies on a number of short-lived odd nuclei in theN=50 region are described. The 59.6-s ⁹³Ru ground state decay was studied in detail for the first time; in these experiments the 10.8-s activity^93m Ru was discovered. The⁹¹Tc activities were also observed for the first time. The ground state and an isomeric state of this nucleus decay with nearby equal half-lives (3.14 and 3.3-min). The activities^91g Mo (16.6-min) and^95m Mo (65.1-s) have been reinvestigated. A number ofγ-rays, previously erroneously assigned to the⁹¹Mo activities, could be eliminated. A strong similarity is noted for the decay schemes of theN=49 isotones^91m Mo and^93m Ru. The energy of the 1/2^? isomeric state in⁹³Ru and theB(M4)-value of the isomeric transition fit well into the systematics of the previously knownN=49 isotones.     

Partial level density of n-quasiparticle excitations, radiative strength functions and new experimental information on the dynamics of nuclear structure change in the B n range

The most reliable at present values of the level density in the fixed spin window and the sums of radiative strength functions of cascade gamma transitions are obtained from analysis of intensities of two-step cascades excited upon thermal neutron capture for approximately 40 nuclei in the mass range 40 ≤ A ≤ 200. The maximal reliability of these data is provided by the experimental conditions—minimum possible propagation error coefficients and practically unique solution of the problem of determination of gamma decay parameters from measured spectra. The experimental data are approximated by the sum of partial level densities corresponding to excitation of n quasiparticles. Steplike structures in the level density at excitation energies smaller than 3–4 MeV are described with good accuracy as the superposition of two-quasiparticle (three-quasiparticle in odd A nuclei) and vibrational excitations with the coefficient of collective density enhancement K _coll ≈ 10?20. They correspond to excitation-energy-correlated maximum enhancement of the radiative strength functions of primary gamma transitions. The level density at larger excitation energies is well reproduced if the breakup of at least two more Cooper pairs of nucleons is taken into account. The increase in the number of excited quasiparticles in the nucleus corresponds to unconditional reduction of the radiative strength functions of primary gamma transitions of the compound state decay. However, the maximum possible value of partial widths of primary transitions increases regularly with decreasing energy. Some ambiguity in the results of approximation and divergence from existing theoretical ideas of the energy dependence of nucleon correlation functions in an excited nucleus point to the possibility of direct extraction from experiment of fundamentally new information on the structure of excited nuclear levels in the range of the neutron binding energy. These are, first of all, the parameters of dependence of nucleon correlation functions on the excitation energy of the nucleus.     

(π, d) Pick-up reaction

The reaction π + A → d + B at low energy is studied in a one-step DWBA framework. The nuclear structure aspects of the reaction are investigated. The reaction involves mostly neutron or proton pairs of the target nucleus with large total momentum and with total spin equal to zero. In the case of even-even nuclei with a partially filled shell, the coherence of the contributions from different orbitals produces an enhancement of the ground state to ground state transitions. Distortion effects are found to be very large. The final-state interaction is crucial in bringing the magnitude of the differential cross section into satisfactory agreement with the experimental value.     

Analysis of excitation functions from light ion induced reactions in the EXCLUSIVE INDEX model

The previously introduced EXCLUSIVE INDEX model allows to predict the population of 6 residual nuclei including the primary compound nucleus through two stages of the preequilibrium phase. The present version is limited to maximum two-nucleon emission. The preequilibrium ejectiles may reduce the brought-in rotational energy by a model of maximum angular momentum decoupling. Subsequent evaporation of protons, neutrons andα-particles is treated in the frame of the Weisskopf-Ewing ands-wave approximation considering pairing effects only in compound nucleus state densities. The sensitivity of essential preequilibrium parameters on the shape of calculated excitation functions is tested. The model predictions well compare to excitation functions fromp, d,³He and⁴He induced reactions including the large set from the reaction⁹³Nb(⁴He,xn yp) up to 170 MeV bombarding energy. The general importance of two-nucleon preequilibrium emission is accentuated in several examples. The deduced preequilibrium parameters corroborate the results from the INDEX model analysis of nucleon spectra.