Isospin Term Research Articles

Extended universal decay law formula for the α and cluster decays

The Universal Decay Law (UDL) formula for the alpha and cluster decays is extended to include the effects of the angular momentum and isospin. The parameters for all formulas are obtained by fitting to available experimental data. We also evaluated the uncertainty of the parameters as well as the uncertainties of predictions of the formulas. The rms values are computed and the best rms among them is obtained for the formula including both the angular momentum and isospin terms. The modified UDL formula is applied to get the half-lives of cluster and alpha decays of nuclei. Branching ratios (alpha/cluster) are calculated and compared with experimental ones. The half-lives for heavier cluster decays are obtained by using UDL and new UDL formulas.

Trajectory in 2D plot of isoscalar and isovector densities of Ca48 and Pb208 , and symmetry energy

We propose a new two-dimensional (2D) plotting method of isoscalar-isovector (IS-IV) densities of $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ to extract not only empirical symmetry energy coefficients $J, L$, and ${K}_{\mathrm{sym}}$ but also the asymmetric isospin term ${K}_{\ensuremath{\tau}}$ in the nuclear incompressibility. We adopted several modern relativistic and nonrelativistic energy density functional (EDF) for the theoretical calculations of IS and IV densities to compare with experimental neutron and proton density distributions determined by recent proton elastic scatterings. We found very strong correlations between the trajectory of the 2D density at the density $\ensuremath{\rho}=0.1\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$ and the symmetry energy coefficients $J, L$, and also ${K}_{\ensuremath{\tau}}$. For ${K}_{\mathrm{sym}}$, the Skyrme EDF SAMi-J family shows a strong correlation in the trajectory of 2D density, while the RMF Lagrangian DDME-J family shows a peculiar quadratic curve and does not provide the experimental value. The symmetry energy term ${K}_{\ensuremath{\tau}}$ of nuclear incompressibility is also discussed in term of the slope of 2D trajectory.

Shell and isospin effects in nuclear charge radii

The shell effect and isospin effect in nuclear charge radii are systematically investigated, and a four-parameter formula is proposed for the description of the root-mean-square (rms) charge radii by combining the shell corrections and deformations of nuclei obtained from the Weizs\"acker-Skyrme mass model. The rms deviation with respect to the 885 measured charge radii falls to 0.022 fm. The proposed formula is also applied for the study of the charge radii of superheavy nuclei and nuclear symmetry energy. The linear relationship between the slope parameter $L$ of the nuclear symmetry energy and the rms charge radius difference of the ${}^{30}\mathrm{S}\ensuremath{-}{}^{30}\mathrm{Si}$ mirror pair is clearly observed. The estimated slope parameter is about $L=54\ifmmode\pm\else\textpm\fi{}19\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ from the coefficient of the isospin term in the proposed charge radius formula.

N=4chiral supermultiplet interacting with a magnetic field

We couple N=4 chiral supermultiplet with an auxiliary N=4 fermionic supermutiplet containing on-shell four physical fermions and four auxiliary bosons. The latter ones play the role of isospin variables. We choose the very specific coupling which results in a component action containing only time derivatives of fermionic components presented in the auxiliary supermultiplet, which therefore may be dualized into auxiliary ones. The resulting component action describes the interaction of the chiral supermultiplet with a magnetic field constant on the pseudo-sphere $SU(1,1)/U(1)$. Then we specify the prepotential of our theory to get, in the bosonic sector, the action for the particle moving over the pseudo-sphere -- Lobachevsky space. We provided also the Hamiltonian formulation of this system and show that the full symmetry group of our system is $SU(1,1)\times U(1)$. The currents forming the $su(1,1)$ algebra are modified, as compared to the bosonic case, by the fermionic and isospin terms, while the additional u(1) current contains only isospin variables. One of the most important features of our construction is the presence in the Hamiltonian and supercharges of all currents of the isospin group SU(2). Despite the fact that two of the su(2) currents ${T,{\bar{T}}}$ enter the Hamiltonian only through the Casimir operator of the SU(2) group, they cannot be dropped out, even after fixing the total isospin of the system, because these currents themselves enter into the supercharges. We also present the Hamiltonian and supercharges describing the motion of a particle over the sphere $S^2$ in the background of constant magnetic field. In this case the additional isospin currents form the $su(1,1)$ algebra.

PROTON STATIC PROPERTIES BY USING HYPERCENTRAL CONSTITUENT QUARK MODEL AND ISOSPIN

The static properties of protons are useful for understanding the quark structure of the proton. In his work we have introduced the hypercentral constituent quark model and isospin dependent potentials. Here constituent quarks interact with each other via a potential in which we have taken into account the three-body force effect and the standard two-body potential contributions. According to our model the static properties of protons containing u and d quarks are better than the other models and closer to experimental results. The two key ingredients of this improvement are the effective quark–gluon hypercentral potentials, and hyperfine interaction and isospin dependence potential. Recently, Schrödinger equation has been solved by Giannini but we have solved the Dirac equation exact analytically and we have shown that a considerable improvement in the description of the static properties of proton is obtained with an isospin dependent potential and the complete interaction including spin and isospin terms reproduces the position of the quark.

A new look at the [formula omitted] baryon multiplet in the [formula omitted] expansion

So far, the masses of excited states of mixed orbital symmetry and in particular those of nonstrange [ 70 , 1 − ] baryons derived in the 1 / N c expansion were based on the separation of a system of N c quarks into a symmetric core and an excited quark. Here we avoid this separation and show that an advantage of this new approach is to substantially reduce the number of linearly independent operators entering the mass formula. A novelty is that the isospin–isospin term becomes as dominant in Δ as the spin–spin term in N resonances.

Contribution of pseudoscalar mesons to ΛN → NN observables within an independent particle shell-model framework

The effect of isospin terms of weak interaction on the main nonmesonic hypernuclear weak decay observables, the total rate, ΓNM, the neutron-to-proton branching ratio, Γn/p, and the proton asymmetry parameter, aΛ, is evaluated. A general shell-model formalism for finite hypernuclei recently developed has been used. A strangeness-changing weak ΛN → NN transition potential including the exchange of pseudoscalar mesons (π, η, K) is adopted. The effects of isospin changes have been added through an adequate modification of the weak coupling constants and a comparison with contribution is made both for 12ΛC and 5ΛHe. Numerical computations show that the effect on the decay rates is very small and the neutron-to-proton ratio is reduced to ∼4%. The asymmetry parameter aΛ is increased in the same percentage. We conclude that the effect of terms helps to enhance the aΛ value but diminishes Γn/p, both by a few per cent. In this regard, contribution of pseudoscalar mesons is not enough to reproduce the experimental data. The necessity of a detailed analysis including vector-meson exchange is suggested.

Calculation of complete fusion cross sections of heavy ion reactions using the Monte Carlo method

The nucleus-nucleus potential for the fusion reactions {sup 40}Ca+{sup 48}Ca, {sup 16}O+{sup 208}Pb, and {sup 48}Ca+{sup 48}Ca has been calculated using the Monte Carlo method. The results obtained indicate that the technique employed for the calculation of the nucleus-nucleus potential is an efficient one. The effects of the spin and the isospin terms have also been studied using the same technique. The analysis of the results obtained for the {sup 48}Ca+{sup 48}Ca reaction reveal that the isospin-dependent term in the nucleon-nucleon potential causes the nuclear potential to drop by an amount of 0.5 MeV. The analytical calculations of the fusion cross section, particularly those at energies less than the fusion barrier, are in good agreement with the experimental data. In these calculations the effective nucleon-nucleon potential chosen is of the M3Y-Paris potential form and no adjustable parameter has been used.

Influence of [formula omitted] terms on s- and p-shell contributions to the asymmetry parameter of [formula omitted] decay

Here is evaluated the effect of the Δ T = 3 2 isospin terms of weak interaction on the asymmetry parameter, a Λ , for proton induced nonmesonic hypernuclear weak decay, Λ p → n p . There has been used a general shell model formalism for finite hypernuclei recently developed. A strangeness-changing weak transition potential including the exchange of pseudoscalar mesons ( π, η, K) is adopted. The effects of Δ T = 3 2 isospin changes have been included through an adequate modification of the weak coupling constants. A comparison with Δ T = 1 2 contribution is made for s- and p-shell hypernuclei. It is analytically shown and numerically corroborated for 12 Λ C and 5 Λ He that Δ T = 3 2 terms affect approximately in the same percentage both s- and p-shell contributions to proton asymmetry parameter. The value of this observable is increased in ∼ 4 % . The effect of Δ T = 3 2 terms helps to enhance the asymmetry parameter value, but is not enough to reproduce the experimental data. The necessity of a similar detailed analysis including vector meson exchange is suggested.

The Nuclear Fragmentation Phase Transition and Rare Isotope Production

Of all phase transitions in nuclear matter, the fragmentation phase transition is perhaps the one for which there is the best experimental evidence as of now. In addition, theoretical models have been developed to a degree where detailed comparisons are possible. With the advent of rare isotope production facilities using projectile fragmentation techniques (NSCL, GSI, ..., and hopefully RIA in the coming decade), the main interest in this field is beginning to shift towards the exploration of the isospin degree of freedom in the nuclear equation of state. Here we employ a statistical multifragmentation model and discuss the connection between the width of the isotope distribution and the isospin term in the nuclear equation of state.

Bose-Einstein correlations and isospin

Bose-Einstein correlations between pions are analysed in terms of isospin. The lack of Bose-Einstein correlation between π + and π 0 is explicitly demonstrated.

Charge exchange in the final state of direct (γ, n) reactions

The two-step charge-exchange contribution coming from a direct (γ, p) reaction followed by a (p, n) transition due to isospin dependence of the optical-model potential is studied for photonuclear reactions. The charge-exchange mechanism appears to be substantial: its contribution is strongly dependent on the rather uncertain isospin term in the phenomenological optical-model potential, but is still insufficient to make the size of the (γ, n) cross section comparable with the (γ, p) one as found experimentally.

Photoproton decay of theSc45giant dipole resonance

The absolute ($\ensuremath{\gamma}, {p}_{0}$) differential cross sections for $^{45}\mathrm{Sc}$ were measured at bremsstrahlung end point energies between 17 and 25 MeV. Using an artificially constructed pseudomonoenergetic photon spectrum, absolute cross sections for various semidirect photoproton reaction channels were also determined. The general structure in the total ($\ensuremath{\gamma}, p$) cross section is discussed in terms of isospin and deformation effects. The direct, preequilibrium and equilibrium contributions to the photoproton decay of the giant dipole resonance equal about 35, 20, and 45%, respectively, of the total energy-integrated ($\ensuremath{\gamma}, p$) cross section. Comparison is made with the predictions of the exciton model.NUCLEAR REACTIONS $^{45}\mathrm{Sc}(\ensuremath{\gamma}, p)$, $E=15.6\ensuremath{-}25$ MeV, $\ensuremath{\theta}=37\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}143\ifmmode^\circ\else\textdegree\fi{}$; measured $\ensuremath{\sigma}(E; \ensuremath{\theta})$ absolutely. Deduced $\ensuremath{\sigma}(E; {p}_{i})$, $\ensuremath{\sigma}(E)$, direct-semidirect cross section, isospin splitting, preequilibrium decay. Natural target.

Effects of deformation on neutron total cross sections of even-ANd and Sm isotopes

Neutron total cross sections of $^{144}\mathrm{Nd}$ and $^{148}\mathrm{Sm}$ and total cross-section differences for the pairs of isotopes $^{144,142}\mathrm{Nd}$, $^{146,144}\mathrm{Nd}$, $^{148,144}\mathrm{Nd}$, $^{150,144}\mathrm{Nd}$, $^{150,148}\mathrm{Sm}$, $^{152,148}\mathrm{Sm}$, and $^{154,148}\mathrm{Sm}$ have been measured at 25 energies from 0.75 to 14 MeV. Each sample consisted of about 40 g of powdered oxide with an isotopic enrichment >94%. For each isotopic pair the total cross-section difference was determined directly by measuring the ratio of transmitted flux for matched samples. This difference was found to have an oscillatory behavior when plotted as a function of incident neutron energy. The oscillations have been explained as a deformation effect qualitatively in terms of the nuclear Ramsauer effect and quantitatively using a deformed optical model potential. Adding two neutrons to a nucleus in this mass region was found to have a different effect on the neutron total cross section than adding two protons. A coupled channel analysis was performed using as input data the present total cross sections, low-energy neutron scattering parameters, and elastic and inelastic (${2}^{+}$) differential cross sections for neutron scattering at 4 and 7 MeV. Excellent total cross-section fits were obtained for the Sm isotopes; however, the total cross-section fits for the Nd isotopes were only fair. Quadrupole deformation parameters have been deduced for all the isotopes studied. The sensitivity of neutron total cross-section differences to this parameter and to the real isospin term of the nuclear potential is discussed.NUCLEAR REACTIONS $^{142,144,146,148,150}\mathrm{Nd}$, ${E}_{n}=0.75\ensuremath{-}13.89$ MeV, $^{148,150,152,154}\mathrm{Sm}$, ${E}_{n}=0.75\ensuremath{-}14.49$ MeV; measured ${\ensuremath{\sigma}}_{n,\mathrm{tot}}(E)$. Enriched targets. Deduced coupled-channel optical-potential parameters, quadrupole deformation parameters.

Neutron-capture resonance parameters and cross sections for the even-A isotopes of cadmium

The neutron-capture cross sections for all the stable even-A isotopes of Cd were measured with high-energy resolution ( Delta E/E<or approximately=0.2%), between 3 and 90 keV neutron energy at the 40 m station of ORELA. Average neutron-resonance parameters were evaluated and differ from previously accepted values. Both s- and p-wave radiative widths decrease strongly between 106Cd and 116Cd as the neutron binding energy decreases. The average p-wave radiative widths are greater than the s-wave radiative widths for all isotopes. This is interpreted in terms of the configurations of the low-lying states. Both s- and p-wave neutron strength functions decrease as neutron number increases. This behaviour is attributed to an isospin term in the absorptive part of the optical-model potential.

Isospin term of the real part of the Lane optical-model potential

Previous neutron differential cross section measurements for Ni, Fe, and Co at 9 MeV are reanalyzed to obtain the isospin term in the real part of the Lane optical model potential employing a surface-centered form factor. The strength determined is 1.4 +- 0.2 MeV. It is further shown that analysis of the data is little affected by the choice of a volume or surface form for the isospin term in the real potential. (AIP)

Polarized electron-nucleus scattering and parity-violating neutral-current interactions

The polarization asymmetry in the scattering of polarized electrons from nuclei coming from the interference between electromagnetic interactions and parity-violating neutral-current interactions is discussed. It is shown how measurements of this asymmetry in various elastic and inelastic electron-nucleus scatterings can be used to determine specific spin and isospin terms in the hadronic neutral current. A specially interesting case would be a measurement in a ${0}^{+}$ \ensuremath{\rightarrow}${0}^{\ensuremath{-}}$ excitation, in which the asymmetry is 100 times larger than usual because the electromagnetic matrix element involves two-photon exchange.

Analog transitions in theA=30system

The $T=1$-ray decay of the ${2}^{+}$, $\ensuremath{\gamma}$ state at ${E}_{x}=4.183$ MeV in $^{30}\mathrm{P}$ was investigated. A new branch (2 \ifmmode\pm\else\textpm\fi{} 1)% to the ${0}^{+}$, $T=1$ state at ${E}_{x}=0.677$ MeV was found. The decay mode is discussed in terms of isospin and an estimate of the lifetime of this state is derived.NUCLEAR REACTION $^{29}\mathrm{Si}(p,\ensuremath{\gamma})$, $E=0.70\ensuremath{-}0.75$ MeV, measured $\ensuremath{\sigma}(E;{E}_{\ensuremath{\gamma}};\ensuremath{\theta})$, deduced $^{30}\mathrm{P}$ level branching. Enriched $^{29}\mathrm{Si}$ target.

Core polarization effects on first-forbidden β-transitions and the analogous E1 γ-transitions

Effective coupling constants g eff for the first-forbidden β-transitions with operators r and σ× r in medium and heavy nuclei were obtained by comparing experimental matrix elements with pairing model calculations. The matrix elements 〈 r〉 were taken from the E1 γ-ray matrix elements for the isobaric analogue states of the parent nuclei. The values g eff/ g are 0.2–0.3 for semi-magic nuclei and 0.4–0.5 for double-magic nuclei. They are analyzed in terms of isospin (spin) core polarizations. A simple expression for g eff is given in a schematic model. The core polarizations explain well the obtained values of g eff. Spin-flip matrix elements 〈↓∥ tir Y 1∥↑〉 were also analyzed. Detailed discussions are given on the possible giant resonances associated with the first-forbidden β-transitions.

Neutron pick-up from the even calcium isotopes

Abstract The (3He, α) reactions have been performed at 13.0 MeV bombarding energy from a target consisting of approximately equal amounts of the five stable even calcium isotopes. Angular distributions for the strongest l n = 3(1 f 7 2 ) , l n = 2( ld 3 2 ) , and l n = 0(2 s 7 2 ) transitions were measured and analysed using the distorted-wave Born approximation. Optical-model parameters were obtained from 13.0 MeV 3He elastic-scattering measurements. An isospin term in the neutron bound-state potential was used in the analysis. Spectroscopic factors were extracted and are compared with other reported values.