Excitation-energy sharing in uranium induced dissipative collisions

Strongly damped collisions were studied in uranium induced reactions on¹¹⁰Pd and¹²⁴Sn target nuclei near the barrier. The excitation-energy splitting was deduced from binary reaction yields and those in which the heavy fragment undergoes sequential fission. For systems with 87≦Z≦95 for the heavy fragment, the excitation energy is concentrated in the lighter nucleus, at best shared equally. The results indicate a non-equilibrated energy dissipation, and support nucleon exchange based on average single-particle strength functions as the underlying dissipation mechanism at the barrier.     

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.     

Electro-optic response of metal halide $$\hbox {CsPbI}_3$$: A first-principles study

In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken ⁴¹Ca with a single neutron in the ⁴⁰Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the core and the single nucleon. By using parametric Nikiforov–Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for ¹⁷O, ⁴¹Ca, ⁴⁹Ca and ⁵⁷Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.     

Shell effects for isovector <Emphasis Type="Italic">l</Emphasis>-forbidden <Emphasis Type="Italic">M</Emphasis>1 transitions in odd nuclei

It is inferred from the analysis of the experimental data that the reduced probabilities of isovector l-forbidden M1 transitions achieve maximum values in nuclei with a magic core. The minimum values are related to γ transitions in nuclei belonging to the region of stable deformation with A ≈ 25. Isovector l-forbidden M1 transitions in mirror nuclei are explored. The ratio of the reduced probabilities for proton and neutron transitions shows the maximum deviation from the theoretical evaluations for the pair of nuclei ⁴¹Ca-⁴¹Sc consisting of the even-even magic core ⁴⁰Ca and one nucleon outside the closed 1d2s shell.     

New magic nuclei and conditions of their formation

The systematic studies of the arrangement features of single-particle nucleon subshells in even-even ^90,92,94,96Zr isotopes and behavior of some known “magicity parameters” in isotopes and isotones neighboring the ⁹⁶Zr nucleus have led to the interpretation of ⁹⁶Zr as a new doubly magic nucleus. Analysis of the structure of nucleon shells in the ⁹⁶Zr nucleus revealed a feature, which consisted in that near the Fermi energy it had filled proton (π1f _5/2) and neutron (v2d _5/2) subshells with an identical and large total momentum j = 5/2, which was called the j-j coupling. Above the π1f _5/2 shell, there is another filled shell (π2p _1/2) with two j = 1/2 protons. Applied to other filled shells, this empirical rule allowed revealing several new nontraditional magic nuclei: ⁹⁶Sr (Z = 38, N = 58), π1f _5/2, v2d _5/2, and v3s _1/2 subshells; ⁵⁴Ca (Z = 20, N = 34), π2p _3/2, v1d _3/2, and v2p _1/2 subshells; a pair of ³⁰Si (Z = 14, N = 16) and ³⁰S (Z = 16, N = 14) nuclei, π1d _5/2, v1d _5/2, and (π/v)2s _1/2 subshells; and a pair of ¹⁴C (Z = 6, N = 8) and ¹⁴O (Z = 8, N = 6) nuclei, 1p _3/2, v1p _3/2, and v2p _1/2 subshells. The existence of the magic nuclei ^52,54Ca is widely discussed in the literature, the possibility of the existence of the other nuclei found is confirmed by the systematics of the behavior of the “magicity” parameters. The fact that shells with some nucleon numbers different from the classical magic numbers are closed may be due to the manifestation of a new type of interaction between nuclear protons and neutrons occupying certain subshells.     

On the quark structure of the lightest nuclei

It is shown that in the 9q- and 12q-systems, i.e.,³He-³He and⁴He nuclei, the most energetically favourable colour magnetic types of symmetry are [f]_cs=[621] and [f]_cs=[82²], which corresponds to the orbital configurationsS ⁵ P ⁴ [52²] _X andS ⁶ P ⁶ [62³] _X . The colour magnetic nucleon attraction associated with these configurations increases as the square of the nucleon number in the sequence²H,³He,⁴He, becoming quite strong in⁴He. This may provide a basis for explaining the “mysterious properties” of³He-³He and⁴He. However, with the further increase in A, the above effect drastically decreases. A qualitative calculation on the quark excitation spectrum for the³H-³He and⁴He nuclei is presented. The⁴He nucleus seems to possess some properties of a “quark magic nucleus”. The experimental situation is discussed.     

Shell structure for deformed nuclear shapes

Eigenvalues for the harmonic oscillator without l·s or l² terms suggest a deformed shell structure for nuclei with axes ratios 2 : 1 and deformation ? = 0.6 with corresponding nucleon “magic numbers” 2, 4, 10, 16, 28, 40, 60, 80 110 and 140, subject to small modifications due to spin-orbit and other correction terms. Experimental evidence of reasonably stable highly deformed structures corresponding to nucleon numbers 16, 20, 28, 40 and 60 (64) is presented. Attempts to calculate the corresponding potential energy surfaces using the Strutinsky shell correction method are described.     

Target fragmentation in proton-nucleus and16O-nucleus reactions at 60 and 200 GeV/nucleon

Target remnants withZ<3 from proton-nucleus and¹⁶O-nucleus reactions at 60 and 200 GeV/nucleon were measured in the angular range from 30° to 160° (?1.7<η<1.3) employing the Plastic Ball detector. The excitation energy of the target spectator matter in central oxygen-induced collisions is found to be high enough to allow for complete disintegration of the target nucleus into fragments withZ<3. The average longitudinal momentum transfer per proton to the target in central collisions is considerably higher in the case of¹⁶O-induced reactions (≈300 MeV/c) than in proton-induced reactions (≈130 MeV/c). The baryon rapidity distributions are roughly in agreement with one-fluid hydrodynamical calculations at 60 GeV/nucleon¹⁶O+Au but are in disagreement at 200 GeV/nucleon, indicating the higher degree of transparency at the higher bombarding energy. Both, the transverse momenta of target spectators and the entropy produced in the target fragmentation region are compared to those attained in head-on collisions of two heavy nuclei at Bevalac energies. They are found to be comparable or do even exceed the values for the participant matter at beam energies of about 1–2 GeV/nucleon.     

Complete destruction of heavy nuclei by hadrons and nuclei

The total disintegration is considered of nuclei with atomic weights ～100 and 200 by high energy hadrons and He⁴, C¹² nuclei with a momentum of 4.5 GeV/c per nucleon. It is shown that mainly nucleons are emitted, and there is no residual nucleus the mass of which is comparable to that of the primary nucleus. The probability of total disintegration is considered as a function of projectile energy and mass. The multiplicity, energy and emission angle of particles are considered as well. It is shown that the density of nuclear matter in the overlap zone of colliding nuclei exceeds the usual one by a factor of ～4. A comparison is made with interaction models. A conclusion is drawn of the collective interaction mechanism (perhaps, of the shock wave type) of particle ejection from the target nucleus at the first stage of interaction and of explosive decay of the residual nucleus at the next one.     

Evidence for a nuclear phase transition in target nuclei after relativistic nuclear interactions

The degree of excitation of the emulsion target nuclei due to nuclear interactions of oxygen and sulfur projectiles at 200 GeV/nucleon incident energy has been investigated. Using the plausible assumption that the numberN _b of slow particles emitted from the struck target nucleus can be interpreted as a measure of the temperatureT of the residual nucleus, we have found that there exists a critical temperatureT _c of the excited target nucleus. For Ag and Br target nuclei this temperature corresponds to <N _b>≌12 and it is attained when the impact parameters are less than about 4 fm.     

Study of isotope shifts,isotone shifts and nuclear compressibility from the analysis of muonic x-ray transitions

Muonic x-ray transitions in various spherical nuclei in the region 13?Z?83 have been analysed and the isotope and isotone shifts in charge radiusR are investigated. AssumingR=r ₀ A ^1/3, the isotopic and isotonic behaviour of the parameterr ₀ (=RA ^?1/3) is also studied. The variation ofr ₀ with mass numberA reveals the variation of average nucleon density, which in turn sheds light on the compressibility of nuclear matter. The isotope and isotone shifts inR exhibit the shell effects in the vicinity of magic neutron and proton numbers: 20, 28, 50, 82 and 126. The results indicate that neutron-proton interaction is maximum at the beginning of a major neutron shell and decreases gradually as the shell gets filled up. The behaviour of parameterr ₀ clearly suggests that low-Z nuclei are highly compressible while high-Z nuclei are more or less incompressible. The parameterr ₀ too is observed to exhibit profound shell effects.     

Nuclear structure studies of the neutron deficientN=50 nucleus96Pd

The neutron deficient nucleus⁹⁶Pd, four proton holes below the doubly magic¹⁰⁰Sn, has been studied in the reaction⁶⁴Zn (³⁶Ar, 2p 2n). Innγ andγγ coincidences levels up to 7 MeV excitation energy were established, and a new neutron core-excited isomer with T_1/2=35(4)ns and g=0.83 (5) was identified. A detailed shell model study yields excellent agreement for states within the π(p_1/2,g_9/2) configuration space but fails to reproduce the isomerism andg-factor for the core-excited state.     

Gamma spectroscopy of neutron-rich nuclei from the vicinity of the “island of inversion” atN=20

Neutron-richsdf shell nuclei produced by deep-inelastic processes in collision of 230 MeV³⁷Cl ions on a thick²⁰⁸Pb target have been studied via in-beam spectroscopic methods. Candidates for negative parity states in³²Si and³²Al have been identified. Yrast states with spins up to 13/2 have been located in the previously unknown³⁷P nucleus.     

Rearrangements in neutron shell closures far from stability

A survey of experimental results obtained at GANIL (Caen, Prance) on the study of the properties of very neutron-rich nuclei (Z = 6–20, A = 20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N = 16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸0 they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behaviour of the two-neutron separation energies S_2n derived from mass measurements gives a very clear evidence for the existence of the new shell closure N = 16 for Z = 9 and 10 appearing between 2s_1/2 and ld_3/2 orbitals. This fact, strongly supported by the instability of C, N and O isotopes with N > 16, confirms the magic character of N = 16 for the region from carbon up to neon while the shell closure at N = 20 tends to disappear for Z ≤ 13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using the in-beam γ-ray spectroscopy are also reported.     

Projectile stopping in nucleus-nucleus and hadron-nucleus collisions at 4.2 and 10 GeV/c per nucleon

The collisions ofp,²H,⁴He and C with carbon and tantalum nuclei at 4.2 GeV/c per nucleon as well as the collisionsp-C andp-Ta at 10 GeV/c from 2-m propane bubble chamber have been studied. New results on nuclear stopping have been obtained from the examination of proton rapidity distributions and average rapidity of leading protons for collisions of various degree of centrality: our study points out that a proton projectile is fully stopped in the centralp-Ta collisions at 4.2 GeV/c but only partly stopped at 10 Gev/c. The proton multiplicity in the centralp-Ta collisions at 10 GeV/c can be described by the binomial distribution,P(n), which expresses the probability that the projectile meetsn protons among the nucleons being along the diameter of a target nucleus.     

A study of the (α, t) reaction on 19F, 27Al, 51V and 59Co

The angular distributions of tritons from the (α, t) reaction on ¹⁹F, ²⁷Al, ⁵¹V and ⁵⁹Co nuclei corresponding to the (0⁺) ground states and (2⁺) excited states in the final nuclei have been measured in the angular range between 15° and 170° at α-particle energies of 25 MeV. For reactions on ²⁷Al and ⁵¹V nuclei, the differential excitation functions have also been obtained at different angles of outgoing tritons at E_α from 20 to 25 MeV. The experimental angular distributions are analysed by the DWBA approximation on the assumption of a nucleon stripping mechanism. The analyses of the present results and the data obtained earlier for the (α, t) reaction on the 1 p shell nuclei, A ? 30, reveal that the distinguishing feature of the reaction under study is the presence of backward angle peaks in the reaction cross section, which appear to be associated with exchange processes. For the (α, t) reaction on the heavier nuclei (A > 30), the dominant mechanism is nucleon stripping.     

Further evidence for a linear relationship between changes in nuclear charge radii and binding energies per nucleon

The comparison of precise isotope shift data of Xe and Ba with the corresponding changes in binding energy per nucleon reveals a linear relationship between Δ2> and Δ(B/A) for even-even nuclei throughout the h_11/2 neutron shell. The last pair, involving the magic neutron number, is an exception to this rule, indicating the existence of a shell-closure effect.     

Nuclear structure of the heavyN=82 isotones:144Sm and146Gd

For single-closed shell nuclei with a large number of extra-protons, outside theZ=50,N=82 double-closed shell nucleus, a standard shell-model calculation yields dimensions of the Hamiltonian matrices beyond the scope of present computer technology. A quasi-particle (QP) calculation however, is able to describe the most important proton-excitations in a much restricted configuration space. Extended BCS+TDA calculations are performed on the single-closed shell¹⁴⁴Sm and¹⁴⁶Gd nuclei with a Gaussian force as effective two-body interaction. The influence of the nonconservation of the exact number of extra-protons in the BCS-approach is studied by performing a projection onto the states with an exact number of extra-protons (BCS+P). The first excited 2⁺, 4⁺ and 6⁺ states in¹⁴⁶Gd are described mainly by the (1g7/2) ₀ ⁸ (2d5/2) ₀ ⁴ \((1h11/2)_{J^\pi }^2 \) configuration.