Isotone Shifts Research Articles

β2 corrections to spherical energy-density functional calculations for root-mean-square charge radii

Root-mean-square charge radii are discussed in terms of spherical Energy Density Functional (EDF) models corrected for quadrupole deformations. Comparisons between experiment and theory are made for the absolute radii of all even-even nuclei, for the isotonic shift between cadmium and tin isotopes, the isotopic shifts of the calcium isotopes and the isotonic shift for nuclei with $ N=28 $. We conclude that the data are well described in this approach, except for the sharp rise just after the neutron magic numbers.

A generalization of the most common subgraph distance and its application to graph editing

We relate the graph editing distance to a generalized weighted version of the most common subgraph distance. To do so, we introduce the new concepts of isotonic shifts and vector weighted graphs. As a consequence we can give a weak but sufficient condition on cost models to result in an edit metric, ensuring the richness of the class of these functions. Moreover, for arbitrary instances we are able to determine a within cubic time computable upper bound on the edit distance, which equals the minimized distance for infinitely many instances.

Analyses of elastically scattered charged pions from calcium isotopes and the 48Ca-54Fe isotone at 180 MeV

The elastic scattering of 180 MeV positively and negatively charged pions, incident on a set of calcium isotopes and the isotone 48 Ca - 54 Fe, has been analyzed within the framework of a recently updated simple local optical potential. This potential, particularly at the tail region, has been originally determined from available phase shifts using inverse scattering theory and the Klein-Gordon equation as a guide. The analysis is carried out with and without considering the squared potential term in the Klein-Gordon equation. Coulomb effects are accounted for by implementing Stricker's prescription. The numerical results for the angular distributions with isotopic and isotonic shifts have been well reproduced. Relative potential differences, in the imaginary part, for π − − 48 Ca, 40 Ca and π + − 54 Fe, 48 Ca also reveal that the neutron distribution in 48 Ca is more extended by about 0.21 fm.

Study of the isotonic shifts of charge form factor for the light proton-rich nuclei

Charge form factors of elastic electron scattering on light proton-rich nuclei on the N = 8 , 10, 20, and 28 isotonic chains are calculated using the relativistic eikonal approximation with the charge density distributions from the RMF model. The results show that the occupation of the 2 s 1 / 2 state by protons has a great influence on the charge density distribution and consequently on the charge form factor. The results can be useful for the study of behavior of the valence-proton wave functions for such light proton-rich nuclei as can be considered as a cluster plus proton(s), and thus the proton-halo phenomenon. And also the results can be used as a very good test of the single-particle motion determined by the mean field model.

MODIFIED BETHE–WEIZSÄCKER MASS FORMULA WITH ISOTONIC SHIFT AND NEW DRIPLINES

Nuclear masses are calculated using the modified Bethe–Weizsäcker mass formula in which the isotonic shifts have been incorporated. The results are compared with the improved liquid drop model with isotonic shift. Mass excesses predicted by this method compares well with the microscopic–macroscopic model while being much more simple. The neutron and proton drip lines have been predicted using this modified Bethe–Weizsäcker mass formula with isotonic shifts.

Plasma constituents during incremental treadmill exercise in intact and splenectomised horses

Six intact and 6 splenectomised mares were given an incremental exercise test on a treadmill to examine the fluid and electrolyte changes associated with exercise and the role of the spleen in these changes. Blood samples were obtained at rest and at the end of each 1-min step of the test. Exercise at 7 m/sec caused significant (P < 0.05) increases in plasma osmolality (intact, +9.9%; splenectomised, +6.2%), plasma protein concentration (intact, +15.8%; splenectomised, +11.4%), and plasma K+ concentration (intact 46%; splenectomised, +57%). Plasma Na+ concentration did not increase significantly (P > 0.05) in either group (intact = 2.7%; splenectomised, = 3.5%). This appears to be the first record of substantial changes of these constituents during short-term exercise, even before the onset of visible sweat losses. The changes in the concentration of plasma protein suggest that short-term exercise causes a decrease in plasma volume. The changes in the concentration and content of sodium suggest that this is an isotonic shift of fluid. The increase in plasma potassium concentration appears to be due to haemoconcentration as well as an increase in the content of potassium within the vascular compartment.

Behavior of the nuclear charge radii systematics in the s-d shell from muonic atom measurements.

The present work extends the systematics of nuclear charge radii obtained by the method of muonic atoms to nuclei with 8\ensuremath{\le}Z,N\ensuremath{\le}20. The accuracy of the measured muonic Lyman transition energies of generally \ensuremath{\le}10 eV leads to a precision in the model-independent nuclear charge radii differences of 2--3 am for the isotope shifts and 4--9 am for isotone shifts. Both isotope and isotone shifts within the s-d shell behave ``anomalously'' with respect to the systematics of heavier nuclei. However, such behavior is predicted on theoretical grounds, if mixing in the s-d shells and the strong deformation of some of the nuclei in this region are considered. We compare charge radii from elastic electron scattering data with muonic atom rms radii and suggest that observed deviations are possibly due to incomplete dispersion corrections.

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 charge distributions in1f72-shell nuclei from muonic x-ray measurements

Precise $2p\ensuremath{-}1s$ muonic x-ray transition energies and energy shifts were measured for the $1{f}_{\frac{7}{2}}$-shell nuclei $^{39,41}\mathrm{K}$, $^{40,42,43,44,46,48}\mathrm{Ca}$, $^{45}\mathrm{Sc}$, $^{46,47,48,49,50}\mathrm{Ti}$, $^{51}\mathrm{V}$, $^{50,52,53,54}\mathrm{Cr}$, $^{55}\mathrm{Mn}$, and $^{56}\mathrm{Fe}$. The data were analyzed in terms of the Barrett moments $〈{r}^{k}{e}^{\ensuremath{-}ar}〉$ of the nuclear charge distribution, from which equivalent nuclear radii ${R}_{k}$ and isotopic and isotonic differences $\ensuremath{\Delta}{R}_{k}$ were computed. For those nuclei for which electron-scattering data were available, model-independent rms radii and radius differences were deduced from a combined analysis of the present data and elastic electron-scattering data. The $\ensuremath{\Delta}N=2$ isotope shifts between even-$A$ nuclei decrease nearly linearly with increasing $N$ and become negative in the second half $24\ensuremath{\le}N\ensuremath{\le}28$ of the $1{f}_{\frac{7}{2}}$ shell; a strong shell-closure effect is evident at $N=28$. The isotope shifts are independent of $Z$, suggesting that the added neutrons interact with the entire proton core rather than with the valence protons. The $\ensuremath{\Delta}Z=2$ isotone shifts between even-$A$ nuclei decrease smoothly and uniformly with increasing $Z$ for $20\ensuremath{\le}Z\ensuremath{\le}28$ and are essentially independent of $N$. Like the isotope shifts, the isotone shifts display a sudden increase at $Z=28$. Both the $\ensuremath{\Delta}N=1$ isotope shifts and the $\ensuremath{\Delta}Z=1$ isotone shifts show pronounced odd-even staggering. A strong correlation is found between nuclear deformation, as revealed by experimental $B(E2)$ values, and the measured isotope and isotone shifts. The measured isotope and isotone shifts, including those for odd-$A$ nuclei, are satisfactorily described by a simple empirical formula. The experimental results were compared with Hartree-Fock calculations; some recent calculations that include ground-state correlations display improved agreement with experiment through the inclusion of these deformation-related effects.NUCLEAR STRUCTURE $^{39,41}\mathrm{K}$, $^{40,42,43,44,46,48}\mathrm{Ca}$, $^{45}\mathrm{Sc}$, $^{46,47,48,49,50}\mathrm{Ti}$, $^{51}\mathrm{V}$, $^{50,52,53,54}\mathrm{Cr}$, $^{55}\mathrm{Mn}$, $^{56}\mathrm{Fe}$; measured muonic x-ray spectra; deduced nuclear charge radii, isotope and isotone shifts; performed model-independent combined analysis of muonic x-ray data and elastic electron scattering data; compared charge parameters with Hartree-Fock and other calculations.

Systematics of nuclear charge distributions in Fe, Co, Ni, Cu, and Zn deduced from muonic x-ray measurements

The results of precise measurements of the energies of the $2{p}_{\frac{3}{2}}\ensuremath{\rightarrow}1{s}_{\frac{1}{2}}$ and $2{p}_{\frac{1}{2}}\ensuremath{\rightarrow}1{s}_{\frac{1}{2}}$ muonic x-ray transitions of $^{54}\mathrm{Fe}$, $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{58}\mathrm{Fe}$, $^{59}\mathrm{Co}$, $^{58}\mathrm{Ni}$, $^{60}\mathrm{Ni}$, $^{61}\mathrm{Ni}$, $^{62}\mathrm{Ni}$, $^{64}\mathrm{Ni}$, $^{63}\mathrm{Cu}$, $^{65}\mathrm{Cu}$, $^{64}\mathrm{Zn}$, $^{66}\mathrm{Zn}$, $^{68}\mathrm{Zn}$, and $^{70}\mathrm{Zn}$, are reported. Using a highly linear digitally stabilized Ge(Li) spectrometer system, the absolute energies and energy shifts between nuclei were measured with total errors of approximately 40-60 eV (110 eV for $^{70}\mathrm{Zn}$). The data were analyzed in terms of the Barrett moments $〈{r}^{k}{e}^{\ensuremath{-}ar}〉$ of the nuclear charge distributions from which the equivalent nuclear radii ${R}_{k}$ and the isotopic and isotonic differences $\ensuremath{\delta}{R}_{k}$ were computed. Particular attention was given to higher-order corrections of the energies of the muonic states. Appropriate quantum-electrodynamical corrections were calculated to all significant orders. Nuclear polarization corrections for multipole interactions up to and including $L=4$ were computed for each isotope. The $\ensuremath{\Delta}A=2$ isotone shifts $\ensuremath{\delta}{R}_{k}$ for even $A$ isotopes show a strong shell closure effect at $Z=28$, which is quite independent of the neutron number. The $\ensuremath{\Delta}N=2$ isotope shifts between even nuclei decrease smoothly and uniformly with increasing $N$ from $N=28$ to $N=40$ and are essentially independent of $Z$. This unexpected behavior suggests that the added neutrons interact with the entire proton core rather than with the valence protons. The $\ensuremath{\Delta}N=1$ isotope shift results show a pronounced odd-even staggering effect, which, however, is somewhat smaller than theoretical predictions. The isotone series $^{58}\mathrm{Fe}$-$^{59}\mathrm{Co}$- $^{60}\mathrm{Ni}$, which is just below the $Z=28$ shell closure, shows strong odd-even staggering, whereas the series $^{64}\mathrm{Ni}$- $^{65}\mathrm{Cu}$-$^{66}\mathrm{Zn}$ and $^{62}\mathrm{Ni}$-$^{63}\mathrm{Cu}$- $^{64}\mathrm{Zn}$ just above $Z=28$ exhibit only a very small staggering effect. A comparison of the experimental data of the rms radii ${〈{r}^{2}〉}^{\frac{1}{2}}$ with the results of spherically constrained Hartree-Fock calculations shows good agreement for all four Zn isotopes and the heavier Ni isotopes ($^{60}\mathrm{Ni}$, $^{62}\mathrm{Ni}$, $^{64}\mathrm{Ni}$), but poor agreement for the Fe isotopes and $^{58}\mathrm{Ni}$.NUCLEAR STRUCTURE, MOMENTS $^{54,56,57,58}\mathrm{Fe}$, $^{59}\mathrm{Co}$, $^{58,60,61,62,64}\mathrm{Ni}$ $^{63,65}\mathrm{Cu}$, $^{64,66,68,70}\mathrm{Zn}$; measured muonic x-ray spectra; deduced nuclear charge parameters, isotope and isotone shifts. Calculated quantum-electrodynamic and nuclear-polarization corrections. Compared charge parameters with Hartree-Fock calculations.

Droplet model isotope shifts and the neutron skin

The isotope and isotone shifts in the nuclear charge radius and the thickness of the neutron skin are calculated for nuclei along beta stability by means of the droplet model.

Precise MuonicKαIsotope Shifts for Nuclides from Si to Sn

Measurements of muonic $K\ensuremath{\alpha}$ isotope shifts for 29 nuclides are described in detail. In most cases, these measurements provide unique information on changes in the nuclear charge distribution. The model dependence of the changes in rms radii derived from the muonic shifts (necessary for comparison with electronic data) is discussed in detail. The muonic shifts in Sr, Zr, and Sn are compared with the relevant electronic measurements; the Ca isotope shifts are compared with the results of recent electron scattering results. Strong shell effects are confirmed at $N=28 \mathrm{and} 88$, viz., ${\mathrm{Ca}}^{48}$ and ${\mathrm{Sr}}^{88}$ are found to have smaller rms charge radii than ${\mathrm{Ca}}^{40}$ and ${\mathrm{Sr}}^{86}$. Precise values are also obtained for the K-Ca isotone shifts and for the absolute energies of nine $K\ensuremath{\alpha}$ transitions.