Alpha scattering by heavy nuclei

We develop an approximation scheme to calculate the Glauber amplitude for elastic and inelastic alpha-nucleus scattering. It is rapidly converging and works for any nuclear density. The α-particle density is assumed Gaussian.     

Alpha decay of light nuclei

Theoretical α spectroscopic amplitudes are calculated in jj coupling and isotopic spin formalism. The formulae obtained are applied for calculating the α reduced width amplitudes of the lowest lying 2⁺ levels of ¹⁶O using the shell-model wave functions of Zuker, Buck and McGrory.     

Modern models of radiative strength functions for nuclei of medium atomic mass

Models of radiative strength functions (RSFs) that are currently used to describe experimental data have been considered. Experimental RSFs were derived from the analysis of the (p,γ) reaction on nuclei of medium atomic mass. Experiments were performed using the ESU-5 accelerator (National Scientific Center Kharkov Institute of Physics and Technology) in the range of incident proton energies from 1.5 to 3.1 MeV. The experimental RSFs are compared with the predictions of different theoretical models.     

Alpha decay chains from superheavy nuclei

Magic islands for extra-stable nuclei in the midst of the sea of fission-instability were predicted to be around Z=114, 124 or, 126 with N=184, and Z=120, with N=172. Whether these fission-survived superheavy nuclei with high Z and N would live long enough for detection or, undergo α-decay in a very short time, remains an open question. α-decay half lives of nuclei with 130≥Z≥100 have been calculated in a WKB framework using density-dependent M3Y interaction with Q-values from different mass formulae. The results are in excellent agreement with the experimental data. Fission survived Sg nuclei with Z=106, N=162 is predicted to have the highest α-decay half life (∼3.2 h) in the Z=106-108, N=160-164 region called small island/peninsula. Superheavy nuclei with Z>118 are found to have α-decay half lives of the order of microseconds or less.     

Alpha decay theoretical calculations for 125-neutron nuclei

We have applied the new normalized and an older shell-model alpha decay theory to the calculation of decay rates of three 125-neutron isotones²⁰⁹Po,²¹¹Rn, and²¹³Ra. We also have applied the theory to the 2.1-ms isomer of²¹³Ra and are able thus to select a 17/2?assignment as preferable to the 13/2+ alternative.     

One-quasiparticle strength functions in medium-heavy spherical nuclei

A method to describe quantitatively the one-quasiparticle strength functions is proposed which takes approximately into account the coupling of one-quasiparticle states to many-phonon configurations. The method is used to interpret the appropriate experimental data for medium-heavy spherical nuclei. The results are compared with the calculations made in different theoretical approaches.     

Neutron strength functions in rare earth nuclei

The coupling of the single particle motion of the neutron to other degrees of freedom is studied by the (d, p) reaction leading to highly excited states in rare earth nuclei. Experimental spectra have been obtained with a telescope counter system for 13 rare earth isotopes of Gd, Dy, Er and Yb. The results are compared with calculations based upon the single particle model in a deformed Saxon-Woods potential. The spreading of the single particle strength resulting from the coupling to other degrees of freedom is taken into account in a simple phenomenological way. A qualitative similarity between the experimental and calculated spectra is observed, and the total integrated (d, p) cross section up to the neutron binding energy is reproduced quite closely by the calculations. For a given excitation energy, the amount of structure in the experimental spectrum seems to decrease with neutron number for each element investigated.     

Deformation and shape coexistence in medium mass nuclei

Emerging evidence for deformed structures in medium mass nuclei is reviewed. Included in this review are both nuclei that are ground state symmetric rotors and vibrational nuclei where there are deformed structures at excited energies (shape coexistence). For the first time. Nilsson configurations in odd-odd nuclei within the region of deformation are identified. Shape coexistence in nuclei that abut the medium mass region of deformation is also examined. Recent establishment of a four-particle, four-hole intruder band in the doublesubshell closure nucleus⁹⁶Zr₅₆ is presented and its relation to the Nuclear Vibron Model is discussed. Special attention is given to the N=59 nuclei where new data have led to the reanalysis of⁹⁷Sr and⁹⁹Zr and the presence of the [404 9/2] hole intruder state as isomers in these nuclei. The low energy levels of the N=59 nuclei from Z=38 to 50 are compared with recent quadrupole-phonon model calculations that can describe their transition from near-rotational to single closed shell nuclei. The odd-odd N=59 nuclei are discussed in the context of coexisting shape isomers based on the (p[303 5/2]n[404 9/2])2^– configuration. Ongoing in-beam (t.p conversion-electron) multiparameter measurements that have led to the determination of monopole matrix elements for even-even₄₂Mo nuclei are presented, and these are compared with initial estimates using lBA-2 calculations that allow mixing of normal and cross subshell excitations. Lastly, evidence for the neutron-proton³S₁ force's influence on the level structure of these nuclei is discussed within the context of recent quadrupole-phonon model calculations.Work supported by USDOE contract Nr.W-7405-Eng-48 and NATO Grant Nr.RGO565/82.     

Alpha decay and cluster decay of some neutron-rich actinide nuclei

Nuclei in the actinide region are good in exhibiting cluster radioactivity. In the present work, the half-lives of α-decay and heavy cluster emission from certain actinide nuclei have been calculated using cubic plus Yukawa plus exponential model (CYEM). Our model has a cubic potential for the overlapping region which is smoothly connected by a Yukawa plus exponential potential for the region after separation. The computed half-lives are compared with those of other theoretical models and are found to be in good agreement with each other. In this work, we have also studied the deformation effects on half-lives of cluster decay. These deformation effects lower the half-life values and it is also found that the neutron-rich parent nuclei slow down the cluster decay process. Geiger–Nuttal plots for various clusters are found to be linear and most of the emitted clusters are α-like nuclei.     

Variation of interband interaction strength in odd-A nuclei

Bandcrossing in 31 rotational bands of 25 different odd-A nuclei in the rare-earth region has been analysed by using a two-band mixing formalism with a constant band interaction within the framework of the effective decoupling picture. The interband interaction strengthV between the one-quasiparticle band and the three-quasiparticle band exhibits a variation with the neutron number which is not different from the oscillatory behaviour observed in even-even nuclei and does not show signs of any appreciable phase shifting as predicted by theory. However, the overall range of variation ofV is greater than that observed in even-even systems.     

Distribution of dipole and spin-dipole strength in nuclei

The schematic model of Goswami and Pal is applied to heavy nuclei and the dipole strength is shown to reside in just four non-degenerate levels. The collection of all the strength into a single level is discussed. The distribution of strength due to non-constancy of radial integrals and non-degeneracy of unperturbed particle-hole orbits is demonstrated in “realistic” calculations for ²⁰⁸Pb, ¹³²Sn, ⁹⁰Zr and ⁵⁶Ni. The collection of low energy dipole strength into “mini-resonances” is shown to be sensitive to the mean energy difference between neutron and proton particle-hole states.     

The continuum strength of single-particle states in nuclei

Methods are devised to calculate the continuum strength of neutron valence orbits starting with an empirical optical-model potential. Allowance is made for the fact that the bound-state and real optical-model potentials have a common nonlocal origin. Direct calculations are made for the $\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, 1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{,}\text{and}\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbits of the contribution from the elastic-scattering chann also of the total continuum strength using a spectral representation. As predicted by McKellar and also by an improved perturbation model given here, most of the continuum strength lies in inelastic and rearrangement channels. When combined with 5% missing strength from the NN potential core, the estimated total continuum strength is ?12–15% of the single-particle sum rule, which is compatible with other deductions from experimental data.     

Description of radiative strength functions in deformed nuclei

Radiative strength functions ofE1- andM1-transitions from ground states of doubly even deformed nuclei to states near the neutron binding energyB _n are calculated within the quasiparticle-phonon nuclear model. The wave functions of excited states include one- and two-phonon components. The calculations were made with the Pauli principle being or not included in the two-phonon components of the wave functions. It is shown that the radiativeE1- andM1-strength functions as well as the widths of giant dipole resonances in deformed nuclei are slightly influenced by the two-phonon components of the wave functions and they can be calculated in the RPA. Thek _E1- andk _M1-values are calculated for some deformed nuclei of the rare-earth and actinide region. The calculated values ofk _E1 are 1.5–2 times larger and the values ofk _M1 are somewhat less than the average values obtained in [14] from the analysis of available experimental data.     

Alpha clusters in nuclei with 41 ≦ A ≦ 45

The effect of pairing and surface α-clustering structure was studied by means of a Hamiltonian with pairing and four-body interaction terms in a simple two-level model in odd nuclei with 41 ≦ A ≦ 45. It was shown that the dynamical α-structures can be induced by the pairing correlation alone, but with an unusually large value of the strength G of the pairing interaction. The addition of a small four-body interaction term allowed us to diminish the G-value to a physically reasonable one and, at the same time, to get meaningful α-clustering. The four-body term added to the Hamiltonian is a simplified way to improve, in this respect, the two-body pairing interaction (itself a simplified model interaction). For example, in the ground state of ⁴⁵Ti the “α-clusters” appeared with larger probability than that for separate nucleons, while in ⁴⁵Ca both probabilities are approximately equal. The calculated binding energy was also applied to reproduce the experimental difference of the masses of neighbouring nuclei. With the eigenstates of the Hamiltonian, schematic spectroscopic factors for two-nucleon transfer, α-transfer, and elastic scattering of α-particles were also calculated. Spectroscopic factors for the transitions from ground state to ground state and from ground state to excited state were then used to distinguish between superfluid or normal behaviour of these nuclei. In addition to the superfluidity induced by pairing forces, a superfluidity due to four-body correlations was also predicted.     

Alpha clustering in 4n nuclei from 4He to 40Ca

The α clustering in nuclei from ⁴He to ⁴⁰Ca has been presented on a systematic footing which depicts the similarities from nucleus to nucleus. Here, the isomorphic shell model has been employed, which is a hybrid between the conventional shell model and liquid drop model in conjunction with the nucleon finite size and which, in addition, uses no adjustable parameters. In the framework of the model an α-like particle is defined as four close-by nucleons (two neutrons and two protons) in relative angular momentum zero. Thus, up to ⁴⁰Ca nine such α-like particles and two deuterons are formed whose average positions are well specified in the model. Hence, each time an α-like particle is formed (following the aforementioned definition), this could have an average position only at one of the above nine available positions for such particles. Any 4n nucleus arranges its n α-like particles in the same way and any such arrangement corresponds to the ground state or to an excited state of this nucleus and serves as the band head of a rotational band. For ²⁰Ne nine such bands have been found, while for ¹²C and ²⁸Si two and five bands, respectively. The linear α-chain for ¹²C and persisting α-planar structures for heavier nuclei appear in a natural way in the framework of the model and are supported by many observables. The real novelty of this presentation is the fact that the axis of rotation and the number of rotating nucleons inside the same rotational band may change in such a way that the relevant moment of inertia increases monotonically in steps forming for each step a new branch of the band. Thus, several such bands have the same band head, a fact which closely resembles the phenomenon of superdeformation. This phenomenon here is the result of existence of several axes of symmetry and of several axes of rotation which, by changing the axis of rotation, permit the moment of inertia to increase up to the solid body limit.     

Is there neutron-proton pairing in medium heavy nuclei?

Present knowledge of the proton and neutron pairing energies Δ_p and Δ_n, deduced from nuclear masses, is reviewed and an attempt is made to find general trends in the data. The analysis shows that, besides the well-known smooth slow decrease with A, the pairing energies also contain a symmetry energy-like dependence on the neutron excess $\text{(N?Z)}\text{A}$. The trends is most pronounced in the shell 50<Z<82, 82<N<126 where both pairing energies decrease by a factor of almost two between the most neutron deficient and the most neutron rich nuclei. The same tendency persists in other mass regions, but is not a universal one. An empirical expression for Δ, that is more accurate than the value $\text{12A}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{MeV}$ usually assumed, is proposed.     

Effective two-body forces in light and medium mass nuclei

From the spectroscopic information provided by single particle stripping reactions, we have extracted average effective two-body interaction between nucleons in thep-, sd-, andfp- shells. Using the derived interaction parameters, we have calculated the energy centroids of the level spectra of residual nuclei obtained via single nucleon stripping reactions involving light and medium mass nuclei as targets.