Current status and desired precision of the isotopic production cross sections relevant to astrophysics of cosmic rays: Li, Be, B, C, and N

The precision of the current generation of cosmic-ray (CR) experiments, such as AMS-02, PAMELA, CALET, and ISS-CREAM, is now reaching $\approx 1–3\%$ in a wide range in energy per nucleon from GeV/nucleon to multi-TeV/nucleon. Their correct interpretation could potentially lead to discoveries of new physics and subtle effects that were unthinkable just a decade ago. However, a major obstacle in doing so is the current uncertainty in the isotopic production cross sections that can be as high as 20–50% or even larger in some cases. While there is a recently reached consensus in the astrophysics community that new measurements of cross sections are desirable, no attempt to evaluate the importance of particular reaction channels and their required precision has been made yet. It is, however, clear that it is a huge work that requires an incremental approach. The goal of this study is to provide the ranking of the isotopic cross sections contributing to the production of the most astrophysically important CR Li, Be, B, C, and N species. In this paper, we (i) rank the reaction channels by their importance for a production of a particular isotope, (ii) provide comparisons plots between the models and data used, and (iii) evaluate a generic beam time necessary to reach a 3% precision in the production cross sections pertinent to the AMS-02 experiment. This first road map may become a starting point in the planning of new measurement campaigns that could be carried out in several nuclear and/or particle physics facilities around the world. A comprehensive evaluation of other isotopes $Z\le 30$ will be a subject of follow-up studies.

Figure 1

Evolution of error on the calculated Li flux as if new reactions are measured with a perfect precision. The abscissa labels list the reactions (projectile + target), while the improved precision from a new measurement of the corresponding cross section can be read from the respective ordinate value. The plot is read from left to right, with the first bin giving the currently estimated uncertainty. The error of the calculated Li flux is decreasing as more reactions are well measured. All curves assume $\mathrm{\Delta }{\sigma }_r^{\mathrm{current}}=20\%$ and $\mathrm{\Delta }{\sigma }_r^{\mathrm{new}}\to 0$. (Top) Three calculations based on various combination of errors, namely correlated, uncorrelated, or a mixture of these two. (Bottom) Same as in top panel (pale colors), with the additional results from direct production and $C_{ab}$ coefficients. See text for details.

Figure 2

Contributive and cumulative fractions of reactions for the overall production of secondary LiBeB in GCRs at 10 GeV/nucleon. The labels on the abscissa give the projectile + target combination considered.

Figure 3

Illustration of the different energy dependences of one-step and step-step channels. See text for details.

Figure 4

Flux impact of reactions for Li, Be, B, C, and N, as encoded in the $f_{a\mathrm{H}c}$ coefficients. The figure reads as follows: Projectiles (ordinate) interacting on H lead to fragments (abscissa), whose impact on the flux is given by the color scale from ${10}^{-3}$ to 0.25 as indicated on the right-hand side of each plot. Over- and underflows are set to the maximum and minimum color scale respectively.

Figure 5

Evolution of error on the calculated Li, Be, and B fluxes as if new reactions (from left to right) are measured with a perfect precision. The plot is read from left to right, with the first bin giving the currently estimated uncertainty on the flux (no new cross-section measurement). The three sets of curves correspond to three different assumptions made on the cross-section errors, namely correlated Eq. (8), uncorrelated Eq. (9), or a mixture of these two Eq. (10). The shaded areas is obtained by varying the assumption made on the current uncertainty on all cross section, $\mathrm{\Delta }{\sigma }_r^{\mathrm{current}}$, between $15\%$ and $25\%$. This figure is continued on the next page.

Figure 6

Inelastic cross sections of Li, Be, B, C, and N isotopes in reactions with protons. For the lithium cross section, both ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ are shown. For Be, B, and C cases, only data for isotopes ${}^9\mathrm{Be}, {}^{12}\mathrm{C}$, and natural samples are available. These data are extracted from the information presented in Ref. [153], which was stacked into tables by Mashnik. Further data are from the EXFOR database [154]. Full tables including lower energy data points are available on request. The references are the following: Akhababyan 1979 [173], Afanas 1988 [174], Alakoz 1971 [175], Ashmore 1957 [176], Jaros 1978 [177], Basilova 1966 [178], Batty 1958 [179], Belletini 1966 [180], Bobchenko 1979 [153], Booth 1957 [181], Bowen 1958 [182], Burg 1981 [183], Carlson 1965 [184], Carroll 1978 [185], Cassels 1954 [186], Cester 1958 [187], Chen 1955 [188], Denisov 1973 [189], Faldt 1975 [190], Grchurin 1985 [191], Goloskie 1962 [192], Grigorov 1964 [193], Grigorov 1970 [194], Heckman 1978 [195], Johansson 1961 [196], Kirkby 1966 [197], Kirschbaum 1967 [198], Lindstrom 1975 [199], Longo 1961 [200], McGill 1974 [201], Measday 1966 [202], Millburn 1954 [203], Moskalev 1956 [204], Renberg 1972 [205], Dietrich 2002 [206], Lantz 2005 [207], Trzaska 1991 [208], and Abgrall 2016 [209].

Figure 7

$Z=3$ projectiles: ${}^x\mathrm{Li}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information).

Figure 8

$Z=4$ projectiles: ${}^x\mathrm{Be}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.)

Figure 9

$Z=5$ projectiles: ${}^x\mathrm{B}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information).

Figure 10

$Z=6$ projectiles: ${}^x\mathrm{C}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information).

Figure 11

$Z=7$ projectiles: ${}^x\mathrm{N}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.) This figure is continued on the next page.

Figure 12

$Z=8$ projectiles: ${}^x\mathrm{O}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.) This figure is continued on the next page.

Figure 13

$Z=10$ projectiles: ${}^x\mathrm{Ne}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.) This figure is continued on the next page.

Figure 14

$Z=10$ projectiles: ${}^x\mathrm{Ne}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information).

Figure 15

$Z=12$ projectiles: ${}^x\mathrm{Mg}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.) This figure is continued on the next page.

Figure 16

$Z=13$ projectiles: ${}^x\mathrm{Al}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.)

Figure 17

$Z=14$ projectiles: ${}^x\mathrm{Si}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.)

Figure 18

$Z=26$ projectiles: ${}^x\mathrm{Fe}$ + H $\to {}_Z{}^{A}X$. (See Table 16 for citation codes and associated information.)