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The study illustrates how to calculate (p, n) reaction cross-sections for iodine isotopes using the EMPIRE 3.2.3, ALICE-ASH, and TALYS 1.95 computer programs, along with a developed empirical formula. The excitation functions of ${}^{122}$Te(p, $n{)}^{122}$I, ${}^{123}$Te(p, $n{)}^{123}$I, ${}^{124}$Te(p, $n{)}^{124}$I, ${}^{125}$Te(p, $n{)}^{125}$I, ${}^{126}$Te(p, $n{)}^{126}$I, ${}^{128}$Te(p, $n{)}^{128}$I, ${}^{129}$Te(p, $n{)}^{129}$I, ${}^{130}$Te(p, $n{)}^{130}$I and ${}^{131}$Te(p, $n{)}^{131}$I reactions were calculated at incident proton energy ranges of 1–20MeV. The previous calculated data from the evaluated data based on the Evaluated Nuclear Data File (ENDF), such as TENDL-2019, TENDL-2021, MENDL-2, IAEA-Medical and IAEA-Therapeutic, as well as the experimental nuclear reaction cross-section data (EXFOR) about the above reactions, have been collected. The empirical formulas have been compared with computer codes and the experimental and evaluated data found in the EXFOR and ENDF. In general, the calculated, evaluated and experimental ($p,n$) reaction cross-sections are in good agreement.

A semiempirical formula with only three parameters for calculating the logarithm of half-lives of heavy particle emission from a radioactive nucleus is recently proposed. The constants in the formula were obtained by fitting the available data in the trans-actinide region. The suitability of the formula in trans-tin region is studied here. The present study reveals that the semiempirical formula with only three parameters is not agreeing well with other theoretical models in the trans-tin region. Hence, one of the constants proposed earlier which acts a scaling constant is suitably replaced by a quadratic equation. The results are compared with analytical superasymmetric fission model and Shanmugham and Kamalakaran model. The semiempirical formula with new set of constants are found to have a better agreement with the available theoretical results.

A set of empirical formulae have been proposed to calculate the $\alpha$-decay half-lives from ground state to ground state transitions of 356 nuclei classified to different set of e–e, e–o, o–e and o–o isotopes. Within these formulae, modification of the previous set of Royer expressions were done by introducing three different physical terms, including the orbital angular momentum and isobaric asymmetry factors. The predicted $\alpha$-decay half-lives compared with those adopted by former proposed models for the depended experimental data, and significant improvements were noticed for all the studied sets of isotopes.

The systematics of neutron-induced reactions at 14.5MeV are of great importance to describe the excitation of nuclei for the $(n,p)$ reactions. In this study, a new empirical formula is obtained by introducing the proton separation energy to the principal empirical formula for estimating the $(n,p)$ reaction cross-sections for 77 nuclei in the light element mass number range $19\le A\le 101$ at the incident neutron energy of 14.5MeV. The calculated results are compared with the evaluated data declared by the TENDL nuclear data library. The predictions of our formula reveal better agreement with the experimental data than the results obtained from the previous suggested formulae.

Empirical formulas in determining the cross-sections play an important role at the energies of which there are no experimental data scattered about. The purpose of the present communication is to further improve the formulas of the cross-section of $(n,2n)$ reactions at the energies near 14.6MeV. A systematics for the evaluation of these cross-sections is studied. We present the empirical formulas based on the statistical theory of nuclear reactions in connection with the compound nucleus. The new empirical formulas are found by using the experimental cross-sections as a function of the reaction $Q$-value. Thus, the new formulas provide the best description of the existing measured data compared with systematics suggested earlier by other authors.

An empirical formula to calculate the ($n$, $p)$ reaction cross-sections for 14.5MeV neutrons for 183 target nuclei in the range $44\le A\le 212$ is presented. Evaluated cross-section data from TENDL nuclear data library were used to test and benchmark the formula. In this new formula, the nonelastic cross-section term is replaced by the atomic number $Z$, while the asymmetry parameter-dependent exponential term has been retained. The calculated results are presented in comparison with the seven previously published formulae. We show that the new formula is significantly in better agreement with the measured values compared to previously published formulae.

Studies on the cross-sections of (n,n$\alpha$) reactions which are energetically possible, about 14 MeV neutrons are quite scarce. In this paper, the cross-sections of (n,n$\alpha )$ nuclear reactions at $E_n=$14–15 MeV are analyzed by using a new empirical formula based on the statistical theory. We show that neutron cross-sections are closely related to the $Q$-value of nuclear reaction, in particular for (n,n$\alpha$) channels. Results obtained with this empirical formula show good agreement with the available measured cross-section values. We hope that the estimations on the cross-sections using the present formalism may be helpful in future studies in this field.

New empirical formulae for calculating the $(n,p)$ reaction cross-sections were obtained by using the EXFOR experimental data for the neutron energy 14–15MeV. Considering the average binding energy per nucleon and dependences of cross-section in the principal formula, we get empirical formulae for estimating the $(n,p)$ reaction cross-sections for 122 nuclei in the mass number range of $18\le A\le 205$. The EMPIRE 3.2 and TALYS 1.95 codes have been used to evaluate the $(n,p)$ cross-sections for the selected nuclei within the specified neutron energy. The comparison of calculated cross-sections from the present proposed formulae with those from codes and previous systematics reveals more accurate predictions of the experimental data.

In this paper, considering the power of the daughter nuclear charge as a function of the orbital angular momentum taken away by the emitted proton, we propose a formula for the half-life of proton radioactivity. In this formula, we have three coefficients with orbital angular momentum dependence. Using experimentally measured half-lives for 8 proton emitters with $l=0$, 14 proton emitters with $l=2$ and 18 proton emitters with $l=5$, we have obtained the coefficients. The root mean square deviations of our formula respect to the experimental value are found 0.2514, 0.4442 and 0.1846 for emitters $l=0$, 2 and 5, respectively. We have compared our results with Sreeja formula, the semiempirical relation of Hatsukawa and theoretical models such as the Coulomb and proximity potential model (CPPM) and the Gamow-like model. The better agreement with experimental data was observed for our formula in comparison with other theoretical models and Sreeja and Hatsukawa formulas.

Bouncing is a common human activity that is frequently observed in large-span structures such as sports stadiums and concert halls; this activity can cause vibration serviceability problems that must be considered at the structural design stage. Current design codes suggest methods for predicting structural responses under rhythmic bouncing excitations. However, these methods typically do not consider the interaction effect between the crowd and structure, which is highly significant, particularly for large groups of people. Such an effect can quantitatively be evaluated from the structural dynamic property changes attributable to the crowd. Using the random distribution of human model parameters given in a previous study, we propose an empirical formula to predict the frequency and damping ratio of the coupled system via statistical analysis. The structural dynamic properties are updated. A response spectrum method framework that employs the updated structural dynamic properties is proposed and validated through a series of experiments on crowd bouncing. The results show that the response spectrum method provides a reasonable prediction of the structural responses. Hence, this study provides an effective method for quantitatively considering the interaction effect when calculating structural responses at the design stage.

The present study concentrates on the empirical formulas of Goda [1975, 2009]. The formulas were proposed for computing the transformation of three common representative wave heights (i.e. H_1/3, H_max and H_m0) on plane beaches. The objectives of the present study are to verify the Goda formulas for computing the transformation of H_1/3, H_max and H_m0 on unbarred beaches and to extend the formulas for computing the transformation of H_m, H_rms and H_1/10. Laboratory data from small-scale and large-scale wave flumes with unbarred beach conditions are used to verify the formulas. The verification shows that the formulas give very good predictions of H_1/3 and H_m0, but give fair prediction of H_max. The formulas are rewritten in the form of a general formula. The general form of Goda formulas is recalibrated and extended to compute other representative wave heights (i.e. H_m, H_rms and H_1/10). The general formula gives very good predictions of H_m, H_rms, H_1/3, H_1/10, H_max and H_m0.

Realistic force modeling of bone drilling is critical to haptic simulation systems for precise surgical training such as pedicle screw fixation in spine surgery. Existing method of force modeling applied metal machining theory to bone drilling directly. However, the mechanical property of bony material is different from continuous metal. In this paper, we present a novel force modeling method of bone drilling based on empirical formula and drilling experiment to provide a force model with high fidelity. A simplified empirical model of drilling in bony material is derived from the empirical formula of metal drilling. To determine the parameters in our empirical model, we construct an experimental system and perform a group of drilling experiments on real bones. We implement our force model in a group of drilling simulations and compare the computational force with the original experimental data to testify its validity.

By using several traditional empirical formulas, the bursting pressures of a kind of special spherical vessels were calculated, a comparison between calculated and tested results was performed, and the features of errors distribution were analyzed. Based on the features of errors distribution, referring to the methods constructing traditional empirical formulas and taking the constituent characteristics of the original formulas into consideration, the traditional empirical formulas were amended and reconstructed. Moreover the amended and reconstructed formulas were validated by experimental data. The validation results indicate that the accuracy of the amended formulas is higher than that of the traditional empirical formulas and the accuracy of the reconstructed formulas is further higher than that of the amended formulas, which implies that the amended and reconstructed formulas are practically useful in design of the discussed special spherical pressure vessels, the related amendment and reconstruction methods are reasonable and can be used in researches of analogous problems. In this paper the amendment case was presented. The reconstruction case will be presented in a subsequent paper.

By using several traditional empirical formulas, the bursting pressures of a kind of special spherical vessels were calculated, a comparison between calculated and tested results was performed, and the features of errors distribution were analyzed. Based on the features of errors distribution, referring to the methods constructing traditional empirical formulas and taking the constituent characteristics of the original formulas into consideration, the traditional empirical formulas were amended and reconstructed. Moreover the amended and reconstructed formulas were validated by experimental data. The validation results indicate that the accuracy of the amended formulas is higher than that of the traditional empirical formulas and the accuracy of the reconstructed formulas is further higher than that of the amended formulas, which implies that the amended and reconstructed formulas are practically useful in design of the discussed special spherical pressure vessels, the related amendment and reconstruction methods are reasonable and can be used in researches of analogous problems. In a previous paper[1] the amendment case was presented, in this paper the reconstruction case was presented.