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Library format:

STARLIB is a next-generation library of thermonuclear reaction and decay rates. Additional information is available in our publication in the Astrophysical Journal Supplement Series. STARLIB incorporates the results of the Monte Carlo based thermonuclear reaction rate evaluation of Iliadis et al., Nucl. Phys. A841, 31 (2010). Unlike other libraries, STARLIB also provides factor uncertainties and probability density functions of reaction rates at each temperature grid point.

For each nuclear reaction, the experimental or theoretical rates listed here refer to "stellar" rates, that is, rates that take into account the thermal population of the interacting nuclei. The "stellar" rates are computed from "laboratory" rates by using a correction factor, called stellar enhancement factor (SEF), which is obtained from Hauser-Feshbach theory [Goriely, Hilaire, and Koning, Phys. Rev. C 78, 064307 (2008)]. Reverse stellar rates are computed from the corresponding forward stellar rates by using normalized partition functions of the nuclei involved in the reaction [Goriely, Hilaire, and Koning, Phys. Rev. C 78, 064307 (2008)], i.e., the tabulated reverse rates already contain the ratio of partition functions. For weak interactions, the tabulated values correspond to "laboratory" rates, i.e., they do not take the thermal population of excited states in the decaying nucleus into account. The decay rates are either adopted from experiment or from theory.

For the modeling of stellar environments that are exposed to elevated temperatures and densities, the rates listed in STARLIB need to be supplemented by information pertaining to (i) "stellar" weak interactions, and (ii) plasma screening.

Header and column format:

STARLIB lists for each reaction a header and three columns.

Header:

spaces 1-35: interaction label, where each nuclide label is right-aligned in a field of 5 characters; the first 15 spaces contain nuclides of the incoming channel, the following 20 spaces contain nuclides in the outgoing channel. The chapter number is listed in the first space, following the convention of JINA REACLIB .

  • Example 1: the reaction 3He+7Be → 2p+4He+4He is denoted by:
      he3  be7    p    p  he4  he4
  • Example 2: the reaction 4He+104Rb → 107Y+n is denoted by:
      he4rb104    n y107
  • Example 3: the photodisintegration 49Ti → 48Sc+p is denoted by:
     ti49    p sc48
  • Example 4: the beta-decay 99As → 99Se is denoted by:
     as99 se99

Next in the header is the source label indicating the source of the rates. This label occupies spaces 44-47. The labels and the associated references are listed at the end of this page. Space 48 is reserved for a special label: (i) The character "v" denotes a reverse rate that was calculated from the corresponding forward rate; the tabulated values already contain the ratio of partition functions; (ii) "w" denotes a weak interaction; (iii) "g" denotes a gamma-ray transition, see below. The characters "ec" in spaces 46-47 are used for three interactions: the pep reaction; 3He → t; 7Be → 7Li. In these three cases the tabulated rates need to be corrected for the electron density, i.e., multiplied by rho*Ye; this is a legacy from the Caughlan and Fowler compilation.

Next in the header is the nuclear energy release (Q-value) for the interaction in units of MeV. The energy occupies spaces 53-64.

Columns:

column 1 lists the temperature in units of GK (109 K). The lowest and highest temperatures given are 1 MK and 10 GK, respectively.

column 2 lists the thermonuclear rate of a reaction (in units of cm3 mol-1 s-1), or the decay constant of a photodisintegration or a beta-decay (in units of s-1).

column 3 lists the factor uncertainty of the rate at the given temperature.

In most cases it can be assumed that the rate probability density function is described by a lognormal distribution [Longland et al., Nucl. Phys. A841, 1 (2010) Sec. 5.4]. Thus the values of the rate in column 2 and of the corresponding factor uncertainty in column 3 allow an estimation of the lognormal parameters mu and sigma of the rate probability density function at each temperature. They are simply given by:

mu = ln(rate)
sigma = ln(factor uncertainty)

where "ln" denotes the natural logarithm.

Notes:

  1. In one case, the same interaction label appears twice in STARLIB, but the source label is different:
    both the p+p reaction and the p+e+p reaction have the interaction label "    p    p    d". In the first case, the source label is "nacr" (indicating that the rate is adopted from the NACRE evaluation), while in the second case the source label is "ec" (indicating that the rate tabulated here needs to be multiplied by rho*Ye before use in a reaction network calculation).
  2. The nucleus 8Be does not occur in STARLIB. Since its half-life is very short, the breakup into two alpha particles is explicitly included in the tabulated rates. For example, for the triple alpha reaction the total 3a → 12C rate is listed, but not the individual rates for the two steps a+a → 8Be and 8Be+a → 12C.
  3. When a rate was estimated using the Monte Carlo procedure [Longland et al., Nucl. Phys. A841, 1 (2010)], the "median rate" is listed here, not the rate calculated from the parameter mu of the lognormal approximation of the rate probability density.
  4. For the Monte Carlo based rates, the factor uncertainty given here is calculated from f.u. = exp(sigma), where sigma is the spread parameter of the lognormal approximation of the rate probability density.
  5. When incorporating experimental reaction rates published in the literature that were not obtained using the Monte Carlo procedure, we explicitly assume that the rate probability densities are lognormally distributed and find the recommended rate (column 2) and factor uncertainty (column 3) from Eq. (39) of [Longland et al., Nucl. Phys. A841, 1 (2010)].
  6. For experimental beta-decays and competing beta-delayed particle decays, we assume that the rate probability densities are lognormally distributed. Values of the rate and factor uncertainty are computed from the following input: total half-life; uncertainty in half-life; branching ratio, uncertainty in branching ratio.

Beta decays:

Many experimental half-lives in G. Audi's 2003 evaluation were "symmetrized", i.e., they must have been obtained from widths, giving rise to asymmetric uncertainties, and the deduced half-life uncertainties were then made symmetric [the procedure is described in Audi et al., Nucl. Phys. A 729, 3 (2003)]. As a reasonable thing to do, we interpret the reported values of the experimental half-life and its uncertainty (or the derived partial half-life and uncertainty) as the expectation value, E[x], and standard deviation, sqrt(V[x]), of a lognormal distribution. For the decay constant, lambda = ln 2/T1/2, we obtain the "median" value from lambda = exp(ln(ln 2) - mu) and the factor uncertainty from f.u. = exp(sigma), where mu and sigma are found from Eq. (27) of Longland et al., Nucl. Phys. A841, 1 (2010).

Above we assume that the decay constant, lambda, is lognormally distributed. We suspect that the probability densities of very precisely measured half-lives are distributed according to a difference of two Poissonians (i.e., counting statistics limited). One may argue, however, that for not too small sample sizes a Poissonian is well approximated by a Gaussian, which in turn can be approximated by a lognormal distribution if the uncertainty is relatively small.

When a beta-delayed particle decay competes with a beta decay, the "partial" half-lives for these competing interactions are found from t1/2 = T1/2 / BR, while the associated uncertainty is found by quadratically adding the individual relative uncertainties.

Isomeric states:

For the special case of 26Al, six different labels are used: al26, al-6, al*6, al01, al02, al03. The first refers to 26Al in thermal equilibrium. The second and third refer to the ground state (Jπ = 5+) and isomeric state (Ex = 228 keV; Jπ = 0+), respectively. The last three denote the excited 26Al levels at Ex = 417 keV, 1058 keV, and 2070 keV.

At high temperatures, the ground and isomeric state in 26Al will be in thermal equilibrium. In that case, the label "al26" (but none of the other 26Al labels!) may be used when constructing the reaction network. At low temperatures, the ground and isomeric state are not in thermal equilibrium and may be considered as separate species. In that case, the labels "al-6" and "al*6" (but not "al26"!) may be used when constructing the reaction network. The temperature boundary above (below) which 26Al is (is not) in thermal equilibrium is about T = 400 MK [Ward and Fowler, Astrophys. J. 238, 266 (1980)]. These are extreme assumptions and a more consistent procedure is to take the equilibration of the 26Al ground and isomeric state explicitly into account (via excitations of higher lying 26Al levels, of which those at Ex = 417 keV, 1058 keV, and 2070 keV are most important). In the latter case, the labels "al-6", "al*6", "al01", "al02" and "al03" (but not "al26"!) may be used when constructing the reaction network.

The necessary gamma- and beta-decay transition strengths were computed by Coc, Porquet and Nowacki, Phys. Rev. C 61, 015801 (1999); Runkle, Champagne and Engel, Astrophys. J. 556, 970 (2001); Gupta and Meyer, Phys. Rev. C 64, 025805 (2001). Values of the decay constants are listed in App. A of Iliadis et al., Astrophys. J. Suppl. 193, 16 (2011).

Rate reference labels (links present):

  1. REACTION RATES BASED ON EXPERIMENT
    cf88 Caughlan & Fowler, At. Data Nucl. Data Tab. 40, 283 (1988) [CF88]
    de04 Descouvemont et al., At. Data Nucl. Data Tab. 88, 203 (2004)
    mc10 Iliadis et al., Nucl. Phys. A 841, 31 (2010) [Monte Carlo rates]
    mc13 Sallaska et al., ApJ Supp. Ser. 207, 18 (2013) [updated Monte Carlo rates]
    nacr Angulo et al., Nucl. Phys. A 656, 3 (1999) [NACRE]
    taex experimental neutron induced rates, extrapolated using TALYS
  2. REACTION RATES BASED ON HAUSER-FESHBACH THEORY
    fkth Cowan, Thielemann, & Truran, Phys. Rep. 208, 267 (1991) [SMOKER]
    taly Goriely, priv. comm.
  3. DECAY RATES BASED ON EXPERIMENT
    au03w Audi et al., Nucl. Phys. A 729, 3 (2003)
    bet-w beta-minus decay
    bet+w beta-plus decay
    ru09w Rugel et al., Phys. Rev. Lett. 103, 072502 (2009)
    wc12w Tuli, wallet charts, National Nuclear Data Center
    be12w Beringer et al. (2012) [PDG]
  4. DECAY RATES BASED ON THEORY
    bkmow Klapdor, Metzinger & Oda, At. Data Nucl. Data Tab. 31, 81 (1984) [beta-minus decay]
    btykw Takahashi, Yamada & Kondo, At. Data Nucl. Data Tab. 12, 101 (1973) [beta-plus decay]
    ec pep reaction; 3He → t; 7Be → 7Li (*)
    il11g Iliadis et al., Astrophys. J. Suppl. 193, 16 (2011)
    ka88w Kajino et al., Nucl. Phys. A 480, 175 (1988) [beta-decay of excited 26Al levels]
    mo92w Moeller et al. (1992) [beta-minus decay]
    mo03w Moeller, Pfeiffer, and Kratz, Phys. Rev. C 67, 055802 (2003)
  5. INDIVIDUAL RATES, MAINLY BASED ON EXPERIMENT
    an06 Ando et al., Phys. Rev. C 74, 025809 (2006)
    ar12 Arnold et al., Phys. Rev. C 85, 044605 (2012)
    bb92 Rauscher et al., Astrophys. J. 429, 499 (1994)
    be01 Beaumel et al., Phys. Lett. B 514, 226 (2001)
    ce14 Cesaratto et al., Phys. Rev. C 88, 065806 (2013)
    cy08 Cybert & Davids, Phys. Rev. C 78, 064614 (2008)
    fu90 Fukugita & Kajino, Phys. Rev. D 42, 4251 (1990)
    ha10 Hammache et al., Phys. Rev. C 82, 065803 (2010)
    il11 Iliadis et al., Astrophys. J. Suppl. 193, 16 (2011)
    im05 Imbriani et al., Eur. Phys. J. A 25, 455 (2005)
    ku02 Kunz et al., Astrophys. J. 567, 643 (2002)
    mafo Malaney and Fowler, Astrophys. J. 345, L5 (1989)
    nk06 Nagai et al., Phys. Rev. C 74, 025804 (2006)
    po13 Pogrebnyak et al., Phys. Rev. C 88, 015808 (2013)
    re98 Rehm et al., Phys. Rev. Lett. 80, 676 (1998)
    rolf C. Rolfs and collaborators
    se04 Serpico et al., J. Cosm. Astropart. Phys. 12, 010 (2004)
    ta03 Tang et al., Phys. Rev. C 67, 015804 (2003)
    wies M. Wiescher and collaborators

Notes: * Values listed need to be multiplied by rho*Ye.



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These pages are maintained by Anne Sallaska and Christian Iliadis, in collaboration with Art Champagne (UNC),
Sumner Starrfield (ASU), and Frank Timmes (ASU). For comments, send a message to the webmaster.

Supported by the National Science Foundation under award number AST-1008355 and by the DOE under grant number DE-FG02-97ER41041.

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