International Journal of Modern Physics E

These lectures, held at a school at the Galileo Galilei Institute for Theoretical Physics, give a survey of the formalism, the methods and achievements of nuclear direct reaction theory. After recapitulating the principles of quantum scattering theory, projection techniques are used to reduce the complexities of nuclear reactions to the manageable level of a set of a few selected coupled channels interacting via effective operators. Direct reactions are introduced as fast reactions proceeding preferentially through the excitation of doorway components of the nuclear many-body configurations, corresponding to a separation of scales in energy and momentum transfer. The concept of the optical model is introduced and applied to elastic scattering on nuclei. The coupled channel T-matrix formalism is discussed for pion-induced reactions on the nucleon. Applications of direct reaction to theory are illustrated for transfer reactions, inelastic scattering, and single and double charge exchange reactions with light and heavy ions.

The inelastic form factors for C2 transition have been studied for even nickel isotopes (${}^{58-64}$Ni) using the form of Tassie shape for ground state charge density distribution. The charge density distribution is investigated using the one- and two-body terms in the cluster expansion. The effect of short-range correlations is included using Jastrow-type correlation function into the two-body density term of the cluster expansion. This concludes that the inserting of the influence of short-range correlations is required for reaching an important adjustment in the calculated elastic and inelastic form factors which explain the data very well at the high momentum transfers ($q\ge 2.5$fm${}^{-1})$.

Excited states in ${}^{126,128}$Xe were populated via ${}^{122}$Sn(⁹Be, 5n$\gamma$) and ${}^{122}$Sn(⁹Be, 3n$\gamma$) fusion-evaporation reactions, respectively, at a beam energy of 48MeV. The electromagnetic (electric or magnetic) nature and multipolarity of some inter-band $\gamma$ rays are determined from linear polarization and angular correlation measurements. Re-measured/newly measured linear polarization asymmetry helps to assign the parity of 2302-keV (${}^{126}$Xe)/2228-keV (${}^{128}$Xe) $I^{\pi }=5^{-}$ state unequivocally.

For the first time, the production of ${\mathrm{\Delta }}^0$ (1232) resonances has been analyzed in minimum bias $n{+}^{12}$C collisions at 4.2GeV/$c$. The value of the mass and width of the ${\mathrm{\Delta }}^0$ resonances as well as the fraction of the negative pions coming from ${\mathrm{\Delta }}^0$ decay obtained in this work in $n{+}^{12}$C collisions coincide within the uncertainties with those extracted earlier in $d{+}^{12}$C collisions at 4.2GeV/$c$ per nucleon. The inclusive cross-section for production of ${\mathrm{\Delta }}^0$ (1232) resonances in $n{+}^{12}$C collisions at 4.2GeV/$c$ is estimated to be ${\sigma }_{\mathrm{\text{incl}}}=57\pm 3$mb. Production of ${\mathrm{\Delta }}^0$ resonances in $n{+}^{12}$C collisions at 4.2GeV/$c$ has been investigated separately in regions of fragmentation of the target and projectile. The mass of the ${\mathrm{\Delta }}^0$ (1232) proved to be the same within the statistical errors in the target and projectile fragmentation regions. The width of the invariant mass spectrum of ${\mathrm{\Delta }}^0$ excited in the projectile region proved to be considerably larger than that in the target fragmentation region, coinciding within statistical errors with that obtained in collisions of free nucleons. The results of the previous experiments, in which production of $\mathrm{\Delta }$ resonances is investigated in the whole phase space (without separating the target and projectile fragmentation regions), can be approximately regarded as the mean values of $\mathrm{\Delta }$ parameters, averaged over those in the target and projectile fragmentation regions.

In this work, we have developed the simulation tools to study the pulse shape of the p-type point contact germanium (pPCGe) detectors. Charge signal pulse has been simulated within the pPCGe detectors, based on the “Shockley–Ramo modeling” and has been compared to the experimentally measured charge signal pulse. We have also utilized the “finite difference method” technique for simulating the electric field within the pPCGe detector volume to study the drifting process of the charge carrier. The simulated charge signal pulse, based on our simulation tools, has been found compatible with the experimental results.

The secondary component of the GW190814 event left us with a question, “whether it is a supermassive neutron star or lightest black-hole?” Recently, Fattoyev et al. obtained an energy density functional (EDF) named as BigApple, which reproduces the mass of the neutron star is 2.60 $M_{\odot }$ which is well consistent with GW190814 data. This study explores the properties of finite nuclei, nuclear matter and neutron stars by using the BigApple EDF along with four well-known relativistic mean-field forces, namely NL3, G3, IOPB-I and FSUGarnet. The finite nuclei properties like binding energy per particle, skin thickness, charge radius, single-particle energy, and two-neutron separation energy are well predicted by the BigApple for a series of nuclei. The calculated nuclear matter quantities, such as incompressibility, symmetry energy and slope parameters at saturation density, are consistent with the empirical or experimental values where ever available. The predicted canonical tidal deformability by the BigApple parameter set is well-matched with the GW190814 data. Also, the dimensionless moment of inertia lies in the range given by the analysis of PSR J0737-3039A.

The advent of technology widened the study of shell closure for nuclei lying far away from the stability line. The classic shell closures are observed to be valid for nuclei near the stability line. The light exotic nuclei exhibit unique behavior compared to those of stable ones. The objective of this work is to study the shell closure in light nuclei near the neutron drip-line to the proton drip-line region. The systematics of two nucleon separation energy difference ($\mathrm{\Delta }S$) between calculated and experimental data are taken as a tool to study the shell closure of light nuclei. Nucleon separation energy is determined using the liquid drop model (LDM) expression with modified asymmetry and pairing energy terms. The light mass numbered isotopes and isotones as a function of even neutron and even proton numbers were considered for this work. The shell structure predicted by $\mathrm{\Delta }S$ systematics is compared with the first excitation energy $E(2^{+})$. The modified LDM is successful in identifying the shell structure properties of light nuclei in exotic region. The study supports the emergence of new shell closure and the disappearance of existing classic shell closure for both neutron and proton numbers. The shell structure predicted by $\mathrm{\Delta }S$ systematics for isotopes (isotones) of magic nucleon number $Z(N)=8,20$ was in agreement with the results of $E(2^{+})$ analysis.

Deuteron elastic scattering from various targets has been reanalyzed in the context of the double folding optical model (DFOM) and the cluster folding model (CFM) over the 8–50MeV energy range. ⁶Li, ⁷Li, ⁹Be and ${}^{11}$B are the four targets considered. In DFOM calculations, the real part of the nuclear potential is constructed based on the M3Y effective interaction in addition to an imaginary volume part which has a conventional Woods–Saxon form to simulate the reduction in flux. Special attention has been paid to the cluster structure of the considered targets which leads in many cases to a significant rise in differential cross-section at backward angles due to different transfer probabilities. Spectroscopic amplitudes for the following configurations: ${}^6\mathrm{\text{Li}}\to d+\alpha$, ${}^7\mathrm{\text{Li}}\to d+{}^5\mathrm{\text{He}}$, ${}^9\mathrm{\text{Be}}\to d+{}^7\mathrm{\text{Li}}$ and ${}^{11}\mathrm{\text{B}}\to d+{}^9\mathrm{\text{Be}}$ are extracted and compared to the previously available reported values. The energy dependence on real and imaginary volume integrals is studied. Using the phenomenological optical model, DFOM and CFM, a reasonable fit for the angular distribution of the various considered nuclear systems was obtained.

In this paper, the transitions between symmetric and asymmetric modes are investigated for the fission of actinides within the scission point model. All effective energies in fission are investigated in detail, separately. This indicates that the interaction energy and the liquid-drop energy do not change much in the symmetric region, so they cannot play a major role in the transition of actinide fission modes. Additionally, the sum of shell correction of complementary fragments at zero excitation energy is plotted over the fission fragment mass numbers. Also, the mass distributions of actinides fission are calculated within the scission point model. There is a good agreement between the calculated mass distribution and the total shell correction distribution. This indicates that the minimum total shell correction energy at the excitation energy corresponds to the maximum mass distribution for actinides fission, especially for the fermium 258 fission. Therefore, the main reason for the formation of fission mode in the actinides fission is the total shell correction energy of the complementary fission fragments at the zero excitation energy.

Level density $\rho (E,N,Z)$ is derived for a nuclear system with a given energy $E$, neutron $N$, and proton $Z$ particle numbers, within the semiclassical extended Thomas–Fermi and periodic-orbit theory beyond the Fermi-gas saddle-point method. We obtain $\rho \propto I_{\nu }(S)/S^{\nu }$, where $I_{\nu }(S)$ is the modified Bessel function of the entropy $S$, and $\nu$ is related to the number of integrals of motion, except for the energy $E$. For small shell structure contribution one obtains within the micro–macroscopic approximation (MMA) the value of $\nu =2$ for $\rho (E,N,Z)$. In the opposite case of much larger shell structure contributions one finds a larger value of $\nu =3$. The MMA level density $\rho$ reaches the well-known Fermi gas asymptote for large excitation energies, and the finite micro-canonical limit for low excitation energies. Fitting the MMA $\rho (E,N,Z)$ to experimental data on a long isotope chain for low excitation energies, due mainly to the shell effects, one obtains results for the inverse level density parameter $K$, which differs significantly from that of neutron resonances.