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Aims: To correlate the effect of previous COVID-19 infection and vaccination on incidence of COVID -19 infection . Study Design: It is a prospective observational study. Place and Duration of Study: Eternal Heart Care Centre and Research Institute, Jaipur, India. Methodology: We included 405 healthcare workers with COVID-19 positive infection, with or without the symptoms. Clinical as well as hematological examination were done. Results: Our study showed 75.6% seropositivity rate even 6 months after vaccination in which seropositivity was significantly higher in people who had past history of COVID-19 .Antibody levels were highest when observed one month after vaccination. A decrease in antibody levels over time after vaccination is observed. Seropositivity rate was significantly higher in people who were less than 40 years old. Conclusion: A decrease in antibody levels over time after vaccination is observed and this showed that the rate of infection decreases after receiving vaccination.

Recently, from the study of the absolute [Formula: see text] values for the ([Formula: see text]–[Formula: see text]) [Formula: see text]2 transitions, the different roles of the triaxiality parameter [Formula: see text] and [Formula: see text] parts were pointed out. Here, the use of the triaxial rotor model expressions for the [Formula: see text]2)s in producing the bell-shaped curve of [Formula: see text] is illustrated. The variation of certain ([Formula: see text]–[Formula: see text]) [Formula: see text] ratios versus [Formula: see text] for the states [Formula: see text] and [Formula: see text] are illustrated, reflecting the two regions of [Formula: see text]. The inter relation of the [Formula: see text] and [Formula: see text] variables is illustrated for the Os isotopes.

The anharmonicity in the [Formula: see text][Formula: see text]Cd, and [Formula: see text][Formula: see text]Te chain of isotopes, which lie close to magic number [Formula: see text], is analyzed from the study of the correlation of the energy levels in the ground band, and some anomalies in the various entities are pointed out. The split of the degeneracy of the phonon triplet and quintuplet is illustrated. Formation of multiple coexisting phonon multiplets, associated with higher lying excited [Formula: see text] and [Formula: see text] states, and intruder states, including 2p4h excitation, with varying deformations, in [Formula: see text]Cd is discussed. The interacting boson model (IBM) is applied for [Formula: see text] [Formula: see text]Cd. The results of a previous study of [Formula: see text] isotones in the dynamic pairing plus quadrupole model are cited for Cd and Te. The problem of collectivity as reflected in the quadrupole moments and [Formula: see text] values is analyzed. The enigma of deformation features in spherical [Formula: see text]Te, reflected in the transition probability [Formula: see text] is resolved. Charge dependence of [Formula: see text]2 transitions for vibrational nuclei, in producing enhanced [Formula: see text] strengths in Te versus Cd is illustrated.

The problem of mismatching of the level energies, in the ground band and the [Formula: see text]-band of triaxially deformed atomic nuclei, as predicted in the rigid triaxial rotor (RTR) approximation of Davydov and Filippov (DF) model, with experiment, is well known. Here, we illustrate the solutions suggested in the literature, and the deviations observed in the converted energy values, from the experiment. We analyze the source of problem of this mismatch with experiment. This enables a physical picture of the DF (or RTR) model spectra. Our analysis will help in understanding the merits and the limitation of the RTR model in this respect.

Recently, we illustrated the use of the $$\gamma $$ –g absolute B(E2) values in the Davydov–Filippov model (DFM), instead of the $$\gamma \! \!-\!\!g\, B(E2)$$ ratios, for analysing the spectral features of the $$(\gamma < 20^{\circ })$$ deformed nuclei. Here, we illustrate the application of the absolute $$\gamma \! \!-\!\!g \, B(E2)$$ values to the triaxial $$(\gamma > 20^{\circ })$$ nuclei to seek the new role of the $$\gamma $$ variable in these nuclei, and to derive the underlying physics. The decrease of the absolute $$\gamma -g\, B(E2)$$ value for $$\gamma > 20^{\circ }$$ , instead of an increase observed for $$\gamma < 20^{\circ }$$ deformed nuclei is explained. The increase of $$B(E2, 2_{\mathrm {\gamma }}- 0_{\mathrm {1}}^{\mathrm {+}})$$ in spite of the negative band mixing parameter, for deformed nuclei, reveals a new view of the band mixing angle, in contrast to its role for the triaxial nuclei. The three moment of inertia in DF model, for $${}^{\mathrm {158}}$$ Dy and $${}^{\mathrm {120}}$$ Xe display their degree of triaxiality.

The cross over of β-, and γ-band at N = 94 in 158Gd signifies a major change in the nuclear structure of Gd isotopes. Using the microscopic dynamic pairing plus quadrupole (DPPQ) model, we reproduce this transition. The spectral features of the K π = 0 3 + , 2 1 + and 4 1 + bands besides the lower three: ground, β- and γ-bands have been analyzed. The B(E2) values from the K π = 0 2 + and K π = 0 3 + bands are analyzed to interpret the nature of these two bands. The K π = 0 2 + band is confirmed as the axially symmetric β-vibration. The K π = 0 3 + band is shown to be collective vibration, but instead of 2β vibration, it indicates very special features with large anharmonicity. The five excited 0 + states below 2.0 MeV identified in 158Gd from ( p , t ) reaction work are also predicted from the DPPQ model. The relative variation of β- and γ-band head energies and of K π = 0 3 + bands, and of K π = 4 + band with neutron number N in 152 - 160 Gd isotopes is reproduced. But the vibrational energy scale of the excited bands remains expanded. The algebraic interacting sd-boson model is also applied for evaluating the energy spectrum and the B(E2) ratios in these K-bands and for prediction of the multi-phonon 0 + states.

The spectra of the isotopes of Zn, Ge and Se in the A = 60 – 80 region of the nuclear landscape display interesting spectral variations with N and Z. At first we study these structures empirically. The state-wise deformation status of each isotope is deduced using the power index formula. The average value of the power index displays the variation with neutron number N. The linear plot of B ( E 2 , 0 1 + → 2 1 + ) versus [ 1 / E ( 2 1 + ) ] for a given Z gives further information on the spectral variation with N. The level energy spectra are used to study the role of the excited bands in the phase transitions and the possible shape co-existence. The common spectral features of the three isotopic chains and some unique features are pointed out from our study and the role of the Nilsson single particle orbits is discussed. A comparison with recent works for Ge and Se isotopes reveals the importance of our empirical studies vis-a-vis the high efficiency experiments and different theoretical interpretations of the shape changes with N and Z and spin.

The constancy of the Grodzins product (GP) E ( 2 1 + ) × B ( E 2 ) ↑ , implies independence from the vibration–rotation status of the nucleus, after allowing for the Z and A dependence. However, in some recent studies, the correlation of the variation of GP, with some collective entities like the N p N n product have been pointed out. This anomaly of the constancy of the GP versus the variation is reviewed here. Detailed analysis of these applications for the violation of the GPR pointed out in these studies is given. Comparison is also made with the linearity relation of B ( E 2 ) ↑ versus 1 / E ( 2 1 + ) plots for a few elements, which provide a simple view of the GP variation with N and Z. The basic physics underlying this rule is presented.

Low lying states of 150Sm have been studied through decay spectroscopy of odd–odd 150Pm, populated with 150Nd(p, n)150Pm reaction at E b e a m = 8.0 MeV using 97% enriched 150Nd target and detecting the γ-rays with the VENUS array comprised of six Compton suppressed Clover HPGe detectors. Nineteen new transitions are placed, four tentative γ-rays are confirmed and eight transitions are found to have altered placements; consequently assigning thirteen new levels to the decay scheme of 150Pm. The spin-parity assignments of the excited levels of 150Sm were made based on logft and angular correlation analysis.

The validity of the extended Grodzins product rule (GPR) for higher spins in the ground bands of even [Formula: see text], even [Formula: see text] nuclei of the light mass region of Cd to Zn chain of isotopes is studied. The plots of [Formula: see text]2, [Formula: see text]) versus [1/[Formula: see text]] ([Formula: see text], 6[Formula: see text] provide test of the linear relationship of the two entities. There seems to be a good correlation of the two entities at these higher spin states for most of the nuclei studied here. The deviations from linearity in specific cases are found to be useful for studying the variations in the nuclear structures involved. From these linearity plots, the structural change at higher spin in some nuclei involving subshell gaps, as reflected in the anomalous rise or saturation, leads to further insight into the under lying microscopic structure.

The Kr isotopes lying in between the lighter isotopes of (Zn, Ge and Se) and the heavier isotopes of (Sr and Zr) in the [Formula: see text]–80 region exhibit very interesting spectral features. The spectra of [Formula: see text]Kr isotopes display a striking contrast from those of Zn, Ge and Se isotopes. The role of spherical and oblate and prolate deformed subshell gaps at specific [Formula: see text] and [Formula: see text] and the resulting re-inforcement are strikingly evident in these contrasting features, with variation in [Formula: see text] or [Formula: see text]. The evolution of the spectral features in Kr isotopes with [Formula: see text] as reflected in the quadrupole deformation, [Formula: see text]-band structures, [Formula: see text]0 decay, [Formula: see text]2) values, [Formula: see text]-softness of the nuclear core and odd–even staggering in [Formula: see text]-bands is studied to explore the role of the under lying nuclear interactions. The correlations with odd–[Formula: see text] isotopes are explored. The shape co-existence displayed in some Kr isotopes is studied. The large deformation observed in the ground bands of [Formula: see text]Kr, as exhibited in the [Formula: see text]2) values, is especially interesting.

The well known, one-parameter Davydov–Filippov model (DFM) or its variants have been used often to study the inter band [Formula: see text]-g B(E2) ratios for the triaxially deformed nuclei. Here, its application for the axially deformed nuclei with [Formula: see text] less than [Formula: see text] is illustrated, which has not received attention so far. Instead of the usual practice of studying the gamma-ground B(E2) ratios, we focus on the absolute B(E2) values in DFM. It offers a wholly new role of the [Formula: see text]-variable in explaining the spectral features of the axially deformed nuclei. Further, it illustrates the intimate relationship of the [Formula: see text] variable and the quadrupole deformation variable [Formula: see text]. Additionally, a unified view of the various differing patterns of the variation of the [Formula: see text]-g B(E2) ratios versus [Formula: see text] is presented.

The recent data on $B(E2)$ values, deduced from the multi-Coulex excitation of the low spin states in the decay of $^{152}\mathrm{Sm}$, and other experimental findings in the last two decades are compared with the predictions from the microscopic dynamic pairing plus quadrupole model of Kumar and Baranger. The 1292.8 keV ${2}^{+}$ state is assigned to the ${{0}_{3}}^{+}$ band, and the $K=2$ assignment of the 1769 keV ${2}^{+}$ state is confirmed. The anomaly of the shape coexistence of the assumed spherical \ensuremath{\beta} band versus the deformed ground band is resolved. The values from the critical point symmetry X(5) support the collective character of the \ensuremath{\beta} band. The problem with the two-term interacting boson model Hamiltonian in predicting \ensuremath{\beta} and \ensuremath{\gamma} bands in $^{152}\mathrm{Sm}$ leads to interesting consequences. The collective features of the second excited ${K}^{\ensuremath{\pi}}=\phantom{\rule{0.16em}{0ex}}{{0}_{3}}^{+}$ band are preferred over the ``pairing isomer'' view. Also the multiphonon nature of the higher lying ${K}^{\ensuremath{\pi}}={{2}_{2}}^{+}\phantom{\rule{0.16em}{0ex}}\ensuremath{\beta}\ensuremath{\gamma}$ band and ${K}^{\ensuremath{\pi}}={4}^{+}$ band are illustrated vis-\`a-vis the new data and the nuclear structure theory.

A host of alternative energy formulae for the ground bands of even Z even N nuclei are available in the literature. The usual approach is to compare the relative numerical accuracy of the predictions of the level energies by these formulae, for varying deformations of the nuclear core and for high spins. The soft rotor formula and variable moment of inertia model, the ab and pq formulae, the rotation vibration interaction and power index formulae are illustrated. Here, a new perspective is presented, with emphasis on the limitation of the region of their physical validity and on deriving useful meaning of their parameters.

In a previous study of the collective multiphonon bands in $^{154}\mathrm{Gd}$, using the microscopic dynamic pairing plus quadrupole model, data for eight $K$ bands were analyzed. In the last four decades, its decay scheme is significantly revised and the nuclear theory has undergone a significant change. Special focus is on new weak intensity transitions in several bands and on the reassigned levels in its decay scheme. The present study represents a detailed revised analysis of the collective even parity bands below 2.1 MeV. Also, a discussion is given on the nature of the ${K}^{\ensuremath{\pi}}={0}^{+}$ excited bands, validity of band mixing approach, and of the assumption of shape coexistence of \ensuremath{\beta} band with ground band. Comparison is made with the $X$(5) analytical symmetry and the algebraic interacting boson model predictions. Discussion of the $2n$ transfer reactions is given. The validity of the multiphonon view of the ${K}^{\ensuremath{\pi}}={4}^{+}$ and ${2}_{2}^{+}$ bands is also studied.

The well-known Grodzins product [Formula: see text]2, 0[Formula: see text]2[Formula: see text] constancy rule was generalized to the Grodzins linearity relation in our recent work in the form of [Formula: see text] versus [Formula: see text] linear plots. In this form, besides testing the linear relation of [Formula: see text]) and kinetic moment of inertia, it also served as a tool for the study of the spectral details of the nuclei, and for the study of the variation of nuclear structure with [Formula: see text] and [Formula: see text] We now study its extension to the intra band [Formula: see text]2 transition from the higher spins of the ground bands of even [Formula: see text] even [Formula: see text] nuclei of the mid-mass region of Xe–Pt chain of isotopes. We use the plots of [Formula: see text]2, [Formula: see text] versus [Formula: see text] [Formula: see text] and 6[Formula: see text] to test their linear relationship. There seems to be a good correlation of the two entities even at the higher spins for all the nuclei studied here. The deviations from linearity in specific cases can be used for studying the nuclear structures involved.

The nuclei in the [Formula: see text] [Formula: see text] and [Formula: see text] regions, lying on both sides of the [Formula: see text]-stability line, continue to be of interest for their complex nuclear structures. The Grodzins product rule (GPR) viz. [Formula: see text], for the ground bands of even-[Formula: see text] even-[Formula: see text] nuclei provides a useful approach to study these structures. The utility of our method, displaying the linear relation of [Formula: see text] to [Formula: see text], is illustrated for the [Formula: see text] Zn to [Formula: see text] Cd series of isotopes. The spread of the data on the linear plots enables a quick view of the shape phase transitions. The role of the shells and the subshells, at spherical and deformed shell gaps for neutrons and protons, with their mutual re-inforcement and the shape phase transition are vividly visible on our plots. The development of collectivity in this region is also linked to the effective number of valence nucleons above the magic number of [Formula: see text], and 28 rather than [Formula: see text], for Mo to Cd isotopes for a microscopic calculation.

The power law expression [Formula: see text] offers a single-term formula with just two parameters for expressing the level energies in the spectra of even-[Formula: see text] even-[Formula: see text] nuclei. Its application to ground band spectra for a wide range of nuclei has been demonstrated in our earlier works. Here, we extend its application to the rotational bands built on an excited state of [Formula: see text] [Formula: see text]-vibration band and [Formula: see text] beta band. A novel assumption of a virtual level with spin zero for [Formula: see text]-bands is made and its validity and use is illustrated. Here, the constancy of the parameters “[Formula: see text]” and “[Formula: see text]” with spin, offers a more realistic view of the dependence of the nuclear core deformation on spin, in the excited bands. Also, it enables a spinwise view, not available in the other energy fit expressions.

In the collective spectra of atomic nuclei, the level energy [Formula: see text] varies with atomic number [Formula: see text] and neutron number [Formula: see text]. Also the [Formula: see text]2 decay-reduced transition probability [Formula: see text] is related to the energy [Formula: see text]. The product [Formula: see text] is constant according to Grodzins product rule, independent of the vibration or rotational status of the nucleus. The product rule is often used for determining [Formula: see text] from the known [Formula: see text]. However, the variation of the product with various parameters is also suggested in the literature. Hence, a detailed global study of this rule for [Formula: see text] region is warranted. We use a novel method of displaying the linear relation of [Formula: see text] with [Formula: see text] for the isotopes of each element (Xe–Pt), instead of their variation with [Formula: see text] or [Formula: see text]. Through our work, we firmly establish the global validity of the Grodzins relation of [Formula: see text], being proportional to the moment of inertia, except for the deviation in specific cases. Our [Formula: see text] versus [Formula: see text] plots provide a transparent view of the variation of the low-energy nuclear structure. This gives a new perspective of their nuclear structure. Also the various theoretical interpretations of [Formula: see text]s and the energy [Formula: see text] are reviewed.

Background: The neutron-rich Ba isotopes with only six valence protons represent the beginning of the collective rotation-vibration band structure. The sharp shape phase transition at $N=88\text{--}90$ observed in Ce-Gd isotones is not exhibited in $^{144\text{--}146}\mathrm{Ba}$, which renders their analysis interesting. Also there are ambiguities in the spin and band assignments.Purpose: To study their spectra empirically and to compare with predictions from an interacting boson model and microscopic dynamic pairing plus quadrupole model to explain the smooth shape transition at $N=88\text{--}90$.Method: We compare the results of the calculation in the interacting boson models (IBM-1) and IBM-2 and the dynamic pairing plus quadrupole model with experiment and illustrate the variation in level structure of the Ba isotopes with N. The absence of sharp phase transition at $N=88\text{--}90$ is examined.Results: The ambiguous spin and parity of levels of the vibrational bands are assigned on the basis of calculated K components and the decay characteristics.Conclusion: The second ${I}^{\ensuremath{\pi}}={2}^{+}$ states in $^{144,146}\mathrm{Ba}$ have $K=0$ predominance, and ${I}^{\ensuremath{\pi}}={2}_{3}^{+}$ states are $K=2$. The smooth transition at $N=88\text{--}90$ is explained.

The α/β Branching Ratio in the Decay Scheme of K-40

Mobile-based technologies have redefined the way in which agriculture is being done in the recent years. Beginning with the short message service and voice-based knowledge delivery, they have crossed leaps and bounds in catering the diverse information needs of farmers who are geographically dispersed. The public extension programmes are often under funded, suffer from weak agricultural research and lack adequate contact to farmers. On this backdrop, the mobile applications have a larger role to play to supplement the extension efforts to reach the farmers. Although communication mediated by mass media were thought to be less effective than individualised approach which demands more cost and time, mobile applications offer some novel and sustainable solutions to disseminate the customised information with a personal touch. This is very critical for livestock sector where information needs of the farmers are unique and instant. With the surge in the use of smart phones as well as mobile applications for agriculture, it is expected that farming can be made more profitable and remunerative in the coming days.

Beyond the shape phase transition from the spherical vibrator to the deformed rotor regime at [Formula: see text], the interplay of [Formula: see text]- and [Formula: see text]-degrees of freedom becomes important, which affects the relative positions of the [Formula: see text]- and [Formula: see text]-bands. In the microscopic approach of the dynamic pairing plus quadrupole model, a correlation of the strength of the quadrupole force and the formation of the [Formula: see text]- and [Formula: see text]-bands in [Formula: see text]Dy is described. The role of the potential energy surface is illustrated. The [Formula: see text] transition rates in the lower three [Formula: see text]-bands and the multi-phonon bands with [Formula: see text] and [Formula: see text] are well reproduced. The absolute [Formula: see text] [Formula: see text] serves as a good measure of the quadrupole strength. The role of the single particle Nilsson orbits is also described.

The proton neutron interacting boson model (IBM-2) has been used to make a systematic study of Strontium isotopes in this mass region of A ~ 80 with 38 N 48 and Z = 38. The three-term Talmi–Otsuka general Hamiltonian in the framework of the neutron proton version of the Interaction boson model was used to perform the calculations. The yrast levels energy are reproduced. The beta and gamma band energy levels also matched well. The reduced transition probabilities were also calculated and were found to be in agreement with the experimental values. In addition, g-factor for the state was evaluated. Possible candidates for mixed symmetry states were also predicted for several nuclei in this isotopic chain.