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We examine implications of angles having their own dimension, in the same sense as do lengths, masses, {\it etc.} The conventional practice in scientific applications involving trigonometric or exponential functions of angles is to assume that the argument is the numerical part of the angle when expressed in units of radians. It is also assumed that the functions are the corresponding radian-based versions. These (usually unstated) assumptions generally allow one to treat angles as if they had no dimension and no units, an approach that sometimes leads to serious difficulties. Here we consider arbitrary units for angles and the corresponding generalizations of the trigonometric and exponential functions. Such generalizations make the functions complete, that is, independent of any particular choice of unit for angles. They also provide a consistent framework for including angle units in computer algebra programs., Comment: 27 pages, 2 figures, editorial changes, references added. Submitted to Metrologia

Tiwari {\it et al.}\ have identified an annual modulation of the $��$-ray flux at the Soudan Underground Laboratory which is strongly correlated to the radon concentration. The $��$-ray flux results from ($��$,$��$) reactions which are induced by the $��$ activity of radon and its daughters. Unfortunately, the quantitative analysis of the $��$-ray flux is based on unrealistic ($��$,$��$) cross sections, and thus the calculated $��$-ray fluxes are not reliable., 3 pages, 1 figure; Phys. Rev. C, accepted for publication

The yrast band in the heavy $N = Z$ nucleus $^{88}$Ru is studied in the framework of the $��$-cluster model in combination with double-folding potentials. It is found that the excitation energies of the yrast band in $^{88}$Ru can be nicely described within the $��$-cluster approach using a smooth and mildly $L$-dependent adjustment of the potential strength. This result is similar to well-established $��$-cluster states in nuclei with a (magic core $\otimes$ $��$) structure. Contrary, the yrast bands in neighboring $N \ne Z$ nuclei deviate from such a typical $��$-cluster behavior. Finally, the $��$-cluster model predicts reduced transition strengths of about 10 Weisskopf units for intraband transitions between low-lying states in the yrast band of $^{88}$Ru., 6 pages, 1 figure, Europ. Phys. J. A, accepted for publication

Cross sections for $^{40}$Ca + $��$ at low energies have been calculated from two different models and three different $��$-nucleus potentials. The first model determines the cross sections from the barrier transmission in a real nuclear potential. Second, cross sections are derived within the optical model using a complex nuclear potential. The excitation functions from barrier transmission are smooth whereas the excitation functions from the optical model show a significant sensitivity to the chosen imaginary potential. Cross sections far below the Coulomb barrier are lower from barrier transmission than from the optical model. This difference is explained by additional absorption in the tail of the imaginary part of the potential in the optical model. At higher energies the calculations from the two models and all $��$-nucleus potentials converge. Finally, in contradiction to another recent study where a double-folding potential failed in a WKB calculation, the applicability of double-folding potentials for $^{40}$Ca + $��$ at low energies is clearly confirmed in the present analysis for the simple barrier transmission model and for the full optical model calculation., 17 pages, 3 figures, accepted for publication in Int. J. Mod. Phys. E

The cross section of the $^{9}$Be(n,$��$)$^{10}$Be reaction was calculated in the direct capture model. All parameters of the calculations were adjusted to properties of the $^{9}$Be + n system at thermal energies. The calculated cross section at thermonuclear energies shows the expected $1/v$ behavior of $s$-wave capture at low energies, but increases towards higher energies as typical $p$-wave capture. Excellent agreement between new experimental data in the astrophysically relevant energy region and the present calculation is found., 7 pages, 3 figures, Phys. Rev. C, accepted for publication

As suggested in a Comment by Peters, Phys.\ Rev.\ C {\bf 96}, 029801 (2017), a correction is applied to the $^{13}$C($��$,n)$^{16}$O data of Harissopulos {\it et al.}, Phys.\ Rev.\ C {\bf 72}, 062801(R) (2005). The correction refers to the energy-dependent efficiency of the neutron detector and appears only above the ($��$,n$_1$) threshold of the $^{13}$C($��$,n)$^{16}$O reaction at about $E_��\approx 5$ MeV. The corrected data are lower than the original data by almost a factor of two. The correction method is verified using recent neutron spectroscopy data and data from the reverse $^{16}$O(n,$��$)$^{13}$C reaction., 5 pages, 2 figures, Phys. Rev. C, accepted for publication

Background: The ($��$,n) and ($��$,$��$) reactions on $^{17,18}$O have significant impact on the neutron balance in the astrophysical $s$-process. In this scenario stellar reaction rates are required for relatively low temperatures below $T_9 \lesssim 1$. Purpose: The uncertainties of the $^{17,18}$O($��$,n)$^{20,21}$Ne reactions are investigated. Statistical model calculations are performed to study the applicability of this model for relatively light nuclei in extension to a recent review for the $20 \le A \le 50$ mass range. Method: The available experimental data for the $^{17,18}$O($��$,n)$^{20,21}$Ne reactions are compared to statistical model calculations. Additionally, the reverse $^{20}$Ne(n,$��$)$^{17}$O reaction is investigated, and similar studies for the $^{17}$F mirror nucleus are provided. Results: It is found that on average the available experimental data for $^{17}$O and $^{18}$O are well described within the statistical model, resulting in reliable reaction rates above $T_9 \gtrsim 1.5$ from these calculations. However, significant experimental uncertainties are identified for the $^{17}$O($��$,n$_0$)$^{20}$Ne(g.s.) channel. Conclusions: The statistical model is able to predict astrophysical reaction rates for temperatures above 1 GK with uncertainties of less than a factor of two for the nuclei under study. An experimental discrepancy for the $^{17}$O($��$,n)$^{20}$Ne reaction needs to be resolved., 10 pages, 9 figures, Phys. Rev. C, accepted for publication

$��$--cluster states in $^{46}$Cr and $^{54}$Cr are investigated in the double-folding model. This study complements a recent similar work of Souza and Miyake \cite{Sou17} which was based on a specially shaped potential. Excitation energies, reduced widths, intercluster separations, and intra-band transition strengths are calculated and compared to experimental values for the ground state bands in $^{46}$Cr and $^{54}$Cr. The $��$-cluster potential is also applied to elastic scattering at low and intermediate energies. Here, as a byproduct, a larger radial extent of the neutron density in $^{50}$Ti is found., 9 pages, 7 figures, Europ. Phys. J. A, accepted for publication

In their recent study Neelam, Shubhchintak, and Chatterjee have claimed that "it would certainly be useful to perform a Coulomb dissociation experiment to find the low energy capture cross section for the reaction" $^{15}$N(n,$��$)$^{16}$N. However, it is obvious that a Coulomb dissociation experiment cannot constrain this capture cross section because the dominating branchings of the capture reaction lead to excited states in $^{16}$N which do not contribute in a Coulomb dissociation experiment. An estimate of the total $^{15}$N(n,$��$)$^{16}$N cross section from Coulomb dissociation of $^{16}$N requires a precise knowledge of the $��$-ray branchings in the capture reaction. Surprisingly, the calculation of Neelam, Shubhchintak, and Chatterjee predicts a strongly energy-dependent ground state branching of the order of 0.05\% to 0.6\% at energies between 100 and 500 keV which is almost 2 orders of magnitude below calculations in the direct capture model. Additionally, this calculation of Neelam, Shubhchintak, and Chatterjee deviates significantly from the expected energy dependence for $p$-wave capture., 2 pages, 1 figure; Phys. Rev. C, Comment, accepted for publication

In a recent review it was shown that the cross sections of $��$-induced reactions in the $A \approx 20 - 50$ mass range follow a general and smooth trend in most cases. For comparison of cross sections of different targets at various energies the method of reduced cross sections $��_{\rm{red}}$ and reduced energies $E_{\rm{red}}$ was used. Four outliers were identified: $^{36}$Ar and $^{40}$Ar with unusally small cross sections and $^{23}$Na and $^{33}$S with unusually large cross sections. New data for $^{23}$Na were presented at this NPA-7 conference; contrary to the previous data, these new data fit into the general systematics. In addition, a relation between the most effective energy $E_0$ for astrophysical reaction rates (the so-called Gamow window) and the reduced energy $E_{\rm{red}}$ is presented., 4 pages, 2 figures, Proc. NPA7, York, 2015; J. Phys. Conf. Series, in print

The doubly-magic nucleus $^{16}$O has a small neutron capture cross section of just a few tens of microbarn in the astrophysical energy region. Despite of this, $^{16}$O plays an important role as neutron poison in the astrophysical slow neutron capture ($s$) process due to its high abundance. We present in this paper a re-evaluation of the available experimental data for $^{16}$O($n,��$)$^{17}$O and derive a new recommendation for the Maxwellian-averaged cross sections (MACS) between $kT$= 5$-$100 keV. Our new recommendations are lower up to $kT$= 60 keV compared to the previously recommended values but up to 14\% higher at $kT$= 100 keV. We explore the impact of this different energy dependence on the weak $s$-process during core helium- ($kT$= 26 keV) and shell carbon burning ($kT$= 90 keV) in massive stars where $^{16}$O is the most abundant isotope., 13 pages, 7 figures; accepted for publication in Astrophys. J. (2016)

$��$-decay properties of the yet unknown nucleus $^{296}$118 are predicted using the systematic behavior of parameters of $��$-nucleus double-folding potentials. The results are $Q_��= 11.655 \pm 0.095$ MeV and $T_{1/2} = 0.825$ ms with an uncertainty of about a factor of 4., 4 pages, 4 figures, Phys. Rev. C, accepted as Rapid Communication

We propose that the SI be modified so that the radian is a base unit. Some of the details and consequences of such a modification are examined.

Background: Because of its half-life of about 35 million years, 92Nb is considered as a chronometer for nucleosynthesis events prior to the birth of our sun. The abundance of 92Nb in the early solar system can be derived from meteoritic data. It has to be compared to theoretical estimates for the production of 92Nb to determine the time between the last nucleosynthesis event before the formation of the early solar system. Purpose: The influence of a low-lying short-lived isomer on the nucleosynthesis of 92Nb is analyzed. The thermal coupling between the ground state and the isomer via so-called intermediate states affects the production and survival of 92Nb. Method: The properties of the lowest intermediate state in 92Nb are known from experiment. From the lifetime of the intermediate state and from its decay branchings, the transition rate from the ground state to the isomer and the effective half-life of 92Nb are calculated as a function of the temperature. Results: The coupling between the ground state and the isomer is strong. This leads to thermalization of ground state and isomer in the nucleosynthesis of 92Nb in any explosive production scenario and almost 100% survival of 92Nb in its ground state. However, the strong coupling leads to a temperature-dependent effective half-life of 92Nb which makes the 92Nb survival very sensitive to temperatures as low as about 8 keV, thus turning 92Nb at least partly into a thermometer. Conclusions: The low-lying isomer in 92Nb does not affect the production of 92Nb in explosive scenarios. In retrospect this validates all previous studies where the isomer was not taken into account. However, the dramatic reduction of the effective half-life at temperatures below 10 keV may affect the survival of 92Nb after its synthesis in supernovae which are the most likely astrophysical site for the nucleosynthesis of 92Nb., Comment: 5 pages, 3 figures; Phys. Rev. C, accepted for publication

Background: The astrophysical $r$-process occurs in an explosive astrophysical event under extremely neutron-rich conditions, leading to (n,$��$)-($��$,n) equilibrium along isotopic chains which peaks around neutron separation energies of a few MeV. Nuclei with larger $Z$ are usually produced by $��^-$-decay, but under certain conditions also $��$-induced reactions may become relevant for the production of nuclei with $Z+2$. Purpose: The uncertainties of the reaction rates of these $��$-induced reactions are discussed within the statistical model. As an example, $��$-induced ($��$,n) and $(��$,$x$n) reaction cross sections for the neutron-rich $^{86}$Se nucleus are studied in detail. Method: In a first step, the relevance of ($��$,n) and $(��$,$x$n) reactions is analyzed. Next the uncertainties are determined from a variation of the $��$-nucleus potential which is the all-dominant parameter for the astrophysical $Z \rightarrow Z+2$ reaction rate. Results: It is found that the $r$-process flow towards nuclei with larger $Z$ is essentially influenced only by the $��$-nucleus potential whereas the other ingredients of the statistical model play a very minor role. This finding is based on the fact that the flow towards larger $Z$ depends on the sum over all ($��$,$x$n) cross sections which is practically identical to the total $��$-induced reaction cross section. Conclusions: $��$-nucleus potentials play an important role under certain $r$-process conditions because the flow towards larger $Z$ depends sensitively on the total $��$-induced reaction cross section. The uncertainty of the reaction rate is about a factor of two to three at higher temperatures and exceeds one order of magnitude at very low temperatures., 7 pages, 3 figures, Phys. Rev. C, accepted for publication

This paper gives the 2006 self-consistent set of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and also may be found on the World Wide Web at physics.nist.gov/constants., 105 pages, 7 figures, 46 tables; describes in detail the 2006 CODATA adjustment of the values of the constants

Levels in $^{17}$O affect the astrophysical s-process in two opposite ways. The neutron production is enhanced by resonances in the $^{13}$C($\alpha$,$n$)$^{16}$O reaction at excitation energies around 7 MeV in $^{17}$O, and the number of available neutrons is reduced by low-lying resonances in the $^{16}$O($n$,$\gamma$)$^{17}$O reaction corresponding to levels in $^{17}$O with excitation energies of $4-5$ MeV. The present work uses the $^{19}$F($d$,$\alpha$)$^{17}$O reaction to determine absolute widths of the relevant levels in $^{17}$O. The results improve the uncertainties of the previously adopted values and resolve a discrepancy between recent studies for the $1/2^+$ level close to the threshold of the $^{13}$C($\alpha$,$n$)$^{16}$O reaction. In addition, improved excitation energies and widths are provided for several states in $^{17}$O up to excitation energies close to 8 MeV., Comment: 5 pages, 2 figures, Phys. Rev. C (in press)

Plans are underway to redefine the International System of Units (SI) around 2018. The New SI specifies the values of certain physical constants to define units. This article explains the New SI in a way that could be used to present it to high-school physics classes.

A simple reduction scheme using so-called reduced energies $E_{\rm{red}}$ and reduced cross sections $��_{\rm{red}}$ allows the comparison of heavy-ion induced reaction cross sections for a broad range of masses of projectile and target and over a wide energy range. A global behavior has been found for strongly bound projectiles whereas much larger reduced cross sections have been observed for weakly bound and halo projectiles. It has been shown that this simple reduction scheme works also well for $��$-particle induced reactions on heavy target nuclei, but very recently significant deviations have been seen for $��$+$^{33}$S and $��$+$^{23}$Na. Motivated by these unexpected discrepancies, the present study analyses $��$-induced reaction cross sections for targets with masses $A \approx 20-50$. The study shows that the experimental data for $��$-induced reactions on nuclei with $A \approx 20-50$ deviate slightly from the global behavior of reduced cross sections. However, in general the deviations evolve smoothly towards lower masses. The only significant outliers are the recent data for $^{33}$S and $^{23}$Na which are far above the general systematics, and some very old data may indicate that $^{36}$Ar and $^{40}$Ar are below the general trend. As expected, also the doubly-magic $^{40}$Ca nucleus lies slightly below the results for its neighboring nuclei. Overall, the experimental data are nicely reproduced by a statistical model calculation utilizing the simple $��$-nucleus potential by McFadden and Satchler. Simultaneously with the deviation of reduced cross sections $��_{\rm{red}}$ from the general behavior, the outliers $^{23}$Na, $^{33}$S, $^{36}$Ar, and $^{40}$Ar also show significant disagreement between experiment and statistical model calculation., 41 pages, 66 figures, EPJA invited review, in press

New experimental data for the $^{33}$S($��$,p)$^{36}$Cl reaction show a very unusual energy dependence. Contrary to common findings for many other $��$-induced reactions, statistical model calculations underestimate the measured cross sections at very low energies. The relatively huge cross sections at these low energies require a significant amount of single-particle strength in the measured energy range which exceeds by far 100% as soon as the additional strength from the competing $^{33}$S($��$,n)$^{36}$Ar reaction is taken into account. In addition, the new data deviate from a general trend for the energy dependence of $��$-induced reaction cross sections., 5 pages, 4 figures, Phys. Rev. C, accepted as Brief Report; misprint (overestimate -> underestimate) "in "Note added in proof" replaced

Angular distributions of elastic $^{140}$Ce($��$,$��$)$^{140}$Ce scattering are analyzed in the framework of the optical model from low energies around the Coulomb barrier up to about 40\,MeV. From the local fits the total reaction cross section $��_{\rm{reac}}$ is extracted. This procedure requires experimental scattering data with small uncertainties. The results for $��_{\rm{reac}}$ are compared to predictions of different systematic global potentials. It is found that the total reaction cross section $��_{\rm{reac}}$ is well predicted from all global potentials under study although the reproduction of the angular distributions is not perfect in all cases. In addition, the lower energy limit for the extraction of $��_{\rm{reac}}$ from elastic scattering angular distributions is analyzed. Finally, the potentials under study are used to calculate the $^{143}$Nd(n,$��$)$^{140}$Ce cross section, and the predictions are compared to experimental data., 11 pages, 7 figures, Phys. Rev. C, accepted for publication

The cross sections of the $^{130}$Sn(n,$��$)$^{131}$Sn and $^{132}$Sn(n,$��$)$^{133}$Sn reactions are calculated in the direct capture model at low energies below 1.5\,MeV. Using recent data from (d,p) transfer experiments on $^{130}$Sn and $^{132}$Sn, it is possible to avoid global input parameters with their inherent uncertainties and to determine all input to the direct capture model by local adjustments. The calculated direct capture cross sections of $^{130}$Sn and $^{132}$Sn are almost identical and have uncertainties of less than a factor of two. The stellar reaction rates $N_A < ��v >$ show a slight increase with temperature. Finally an estimate for the influence of low-lying resonances to the stellar reaction rates is given., 5 pages, 3 figures, Phys. Rev. C, Brief Report, accepted for publication

Elastic scattering data for $^{141}$Pr($��$,$��$)$^{141}$Pr have been analyzed to derive a new energy-dependent local potential for the $^{141}$Pr-$��$ system. This potential is used successfully to predict the cross section of the $^{141}$Pr($��$,n)$^{144}$Pm reaction at low energies where new experimental data have become available very recently. Contrary to various global potentials, this new potential is able to reproduce simultaneously elastic scattering data around and above the Coulomb barrier and reaction data below the Coulomb barrier for the $^{141}$Pr-$��$ system. Reasons for the partial failure of the global potentials are explained by intrinsic properties of the scattering matrix and their variation with energy. The new local potential may become the basis for the construction of a new global $��$-nucleus potential., 12 pages, 8 figures, Phys. Rev. C, accepted

Alpha-decay half-lives for 104,105,106Te and 108,109,110Xe close above the doubly-magic 100Sn are calculated from systematic double-folding potentials. The derived alpha preformation factors are compared to results for 212,213,214Po and 216,217,218Rn above the doubly-magic 208Pb. Alpha-decay energies of Q_alpha = 5.42 \pm 0.07 MeV and 4.65 \pm 0.15 MeV are predicted for 104Te and 108Xe; the corresponding half-lives are T_{1/2} approx 5 ns for 104Te and of the order of 60 \mu s for 108Xe. Additionally, the properties of rotational bands in 104Te are analyzed, and the first excited 2+ state in 104Te is predicted at E_x = 650 \pm 40 keV; it decays preferentially by gamma emission with a reduced transition strength of 10 Weisskopf units to the ground state of 104Te and with a minor branch by alpha emission to the ground state of 100Sn., Comment: 6 pages, 3 figures, to appear in Europ. Phys. J. A; two misprints in Tables 1 and 3 corrected

Systematic alpha-nucleus folding potentials are used to analyze alpha-decay half-lives of superheavy nuclei. Preformation factors of about several per cent are found for all nuclei under study. The systematic behavior of the preformation factors and the volume integrals of the potentials allows to predict alpha-decay energies and half-lives for unknown nuclei. Shell closures can be determined from measured alpha-decay energies using the discontinuity of the volume integral at shell closures. For the first time a double shell closure is predicted for Z_magic = 132, N_magic = 194, and A_magic = 326 from the systematics of folding potentials. The calculated alpha-decay half-lives remain far below one nanosecond for superheavy nuclei with double shell closure and masses above A > 300 independent of the precise knowledge of the magic proton and neutron numbers., Phys. Rev. C, accepted as Rapid Communication; misprint in Eq.(7) corrected in v2

alpha-nucleus potentials are one important ingredient for the understanding of the nucleosynthesis of heavy neutron-deficient p nuclei in the astrophysical gamma-process where these p nuclei are produced by a series of (gamma,n), (gamma,p), and (gamma,alpha) reactions. I present an improved alpha-nucleus potential at the astrophysically relevant sub-Coulomb energies which is derived from the analysis of alpha decay data and from a previously established systematic behavior of double-folding potentials., Comment: 6 pages, 3 figures, accepted for publication in Phys. Rev. C