We used the blast wave model with the Boltzmann–Gibbs statistics and analyzed the experimental data measured by the NA61/SHINE Collaboration in inelastic (INEL) proton–proton collisions at different rapidity slices at different center-of-mass energies. The particles used in this study were ${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, and $\overline{p}$. We extracted the kinetic freeze-out temperature, transverse flow velocity, and kinetic freeze-out volume from the transverse momentum spectra of the particles. We observed that the kinetic freeze-out temperature is rapidity and energy dependent, while the transverse flow velocity does not depend on them. Furthermore, we observed that the kinetic freeze-out volume is energy dependent, but it remains constant with changing the rapidity. We also observed that all three parameters are mass dependent. In addition, with the increase of mass, the kinetic freeze-out temperature increases, and the transverse flow velocity, as well as kinetic freeze-out volume decrease.

Radioactivity in Granites of Pakistan systematically increases from south to north. The Ambella Granite found at the northern edge of Pakistan is highly radioactive. Radioactivity measurements made on, so called, Bajaur Granite, located in northern Pakistan, have been found to be lowest among all the granitic rock of the area. In order to find out the exact nature of Bajaur rocks, mineralogical studies were carried on rock chips and powdered samples. The Bajaur Norite contains plagioclase feldspar more than 45% as the chief constituent. Orthopyroxene and clinopyroxene are 27% and 18%. Quartz, biotite, and some opaque minerals are also found in accessory amounts. Bajaur Granite is in fact not a granite but Norite, which is rich in Na-Ca plagioclase series of feldspars. The plagioclase feldspar rich in Na-Ca are low in radioactivity. Moreover, the average gamma activities of ${}^{226}$Ra, ${}^{232}$Th, and ${}^{40}$K (4.98 ± 0.13 Bqkg ${}^{-1}$, 4.03 ± 0.31 Bqkg ${}^{-1}$, 204.40 ± 4.72 Bqkg ${}^{-1}$ and a total of all three radionuclides are 214.00 ± 5.39 Bqkg ${}^{-1}$) for Bajaur Norites are found too be much less than the average of the world’s Granites. Indoor and outdoor hazard indices of Bajaur Norite are much below building materials used throughout the world and largely beneath their criterion restrictions. As per radiations’ hazards are concerned, the Bajaur Norite as a building stone may be considered as the safest material available in the area that does not pose any radiological hazard.

We present an analysis of the pseudorapidity $\eta$ and transverse momentum $p_T$ distributions of charged hadrons in $pp$ collisions for the kinematic range of $0<p_T<4$ GeV/c and $\left|\eta \right|<2.4$ at 0.9, 2.36, and 7 TeV. Charged particles are produced in $pp$ collision using several Monte Carlo event generators (Pythia Simple, Vincia, Dire showers, Sibyll2.3d, QGSJETII-04, EPOS-LHC) and compared with CMS data at LHC. It is observed that the Simple parton showers can explain the CMS data very well for $p_T>1$ GeV/c at 0.9 and 2.36 TeV within the experimental errors, while Dire overshoots and Vicia undershoots the data by 50% each. At 7 TeV, the Dire module presents a good prediction, whereas the Simple and Vincia modules underestimate the data within 30% and 50%. Comparing the Simple module of the Pythia model and the predictions of the CRMC models with the experimental data shows that at 0.9 TeV, EPOS-LHC has better results than the others. At 2.36 GeV, the cosmic rays Monte Carlo (CRMC) models have better prediction than the Simple module of Pythia at low $p_T$, while QGSJETII-04 predicts well at high $p_T$. QGSJETII-04 and EPOS-LHC have closer results than the Pythia-Simple and Sibyll2.3d at 7 TeV. In the case of the pseudorapidity distributions, only the Pythia-Simple reproduced the experimental measurements at all energies. The Dire module overestimates, while Vincia underestimates the data in decreasing order of discrepancy (20%, 12%, 5%) with energy. All CRMC models underestimate the data over the entire $\eta$ range at all energies by 20%. The angular ordering of partons and the parton fragmentation could be possible reasons for this deviation. Furthermore, we used the two-component standard distribution to fit the $p_T$ spectra to the experimental data and extracted the effective temperature ($T_{eff}$) and the multiplicity parameter ($N_0$). It is observed that $T_{eff}$ increases with the increase in the center of mass energy. The fit yielded $0.20368\pm 0.01$, $0.22348\pm 0.011$, and $0.24128\pm 0.012$ GeV for 0.9, 2.36, and 7 TeV, respectively. This shows that the system at higher energies freezes out earlier than lower ones because they quickly attain the equilibrium state.

The knowledge of beta-decay transitional probabilities and Gamow-Teller (GT) strength functions from highly excited states of nuclides is of particular importance for applications to astrophysical network calculations of nucleosynthesis in explosive stellar events. These quantities are challenging to achieve from measurements or computations using various nuclear models. Due to unavailability of feasible alternatives, many theoretical studies often rely on the Brink-Axel (BA) hypothesis, that is, the response of strength functions depends merely on the transition energy of the parent nuclear ground state and is independent of the underlying details of the parent state, for the calculation of stellar rates. BA hypothesis has been used in many applications from nuclear structure determination to nucleosynthesis yield in the astrophysical matter. We explore here the the validity of BA hypothesis in the calculation of stellar beta-decay (BD) and electron capture (EC) weak rates of fp- and fpg-shell nuclides for GT transitions. Strength functions have been computed employing the fully microscopic proton-neutron QRPA (quasi-particle random-phase approximation) within a broad density, ρY _e = (10-10¹¹) [g cm⁻³], and temperature, T = (1−30) [GK], grid relevant to the pre-collapse astrophysical environment. Our work provides evidence that the use of the approximation based on the BA hypothesis does not lead to reliable calculations of excited states strength functions under extreme temperature-density conditions characteristic of presupernova and supernova evolution of massive stars. Weak rates obtained by incorporating the BA hypothesis in the calculation of strength functions substantially deviate from the rates based on the state-by-state microscopically calculated strength functions. Deviation in the two calculations becomes significant as early as neon burning phases of massive stars. The deviation in the calculation of BD rates is even more pronounced, reaching up to three orders of magnitude.