Nuclear Data Needs for r-Process Calculations

Bradley Meyer

Clemson University

Four Requirements for Meaningful Measurements for Astrophysics (The et al. 1998)

• An appropriate astrophysical model of events significant for nucleosynthesis . (“Appropriate” does not necessarily = “correct”!)

• An observable from the nucleosynthesis process, usually an abundance result that is either known or measurable.

• The dependency of the value of the observable on the value of a nuclear cross section.

• An experimental strategy for measuring that cross section, or at least of using measurable data to better calculate it.

R-Process Observables

• Production of heavy elements:– Neutron-to-seed ratio (~100)

– Dependent on nuclear reactions at T9 > 4

• Details of final abundance distribution– Peaks– Freezeout abundances—smoothing

– Dependent on nuclear reactions for T9<3

Appropriate Model? Which regime?

• Low-entropy r-process

• High-entropy r-process

• High-entropy, fast expansion r-process

Production of heavy nuclei in the first place (n/s~100)

• Depends on weak interaction physics—electron capture rates, neutrino-nucleus interaction rates

• Quasi-equilibrium: nuclear masses and partition functions

• Three-body reaction rates (α+α+α12C, α+α+n9Be and 9Be+α12C+n

• Charged-particle reactions on proton-rich isotopes for the high-entropy, fast expansion regime

Meyer and Wang (2007)

Production of 4He from n, p (T9 = 10 – 8)

ppnn

HepHHenpHnHnp 42332 ),(),(),(),(

Production of 4He from n, p (T9 < 8)

ppnn

NipCupNinNinNi 5659585756 ),(),(),(),(

Too few heavy nucleineutrons and protons don’t assemble intoalpha particles and heavier speciesmany free neutrons and protonsaround to bombard the few heavy nuclei present

Meyer and Wang (2007)

Details of the Final R-Process Abundances

• Depends on:– Nuclear masses– Neutron-capture cross sections– Beta-decay rates– Spins and partition functions– Fission yields

Reference calculation

Neutron-capture cross sections

Beta-decay rates

Spins and Partition Functions

Four Requirements for Meaningful Measurements for Astrophysics (The et al. 1998)

• An appropriate astrophysical model of events significant for nucleosynthesis . (“Appropriate” does not necessarily = “correct”!)

• An observable from the nucleosynthesis process, usually an abundance result that is either known or measurable.

• The dependency of the value of the observable on the value of a nuclear cross section or other nuclear property.

• An experimental strategy for measuring that cross section, or at least of using measurable data to better calculate it.

What is libnucnet?

• A C toolkit for storing and managing nuclear reaction network.

• Built on top of libxml (the gnome XML parser and toolkit) and gsl (the GNU scientific library).

• Released under the GNU General Public License.

History of libnucnet

• Original goal—online nucleosynthesis tool• Problem—input over the web• Solution—XML (eXtensible Markup Language)• Libxml as input and output• Libxml has powerful built-in data structures (lists,

hashes, trees, etc.)—build new nucleosynthesis code on top of libxml

• Hashes provide easy access to data—particularly useful for experimentalists

Features of libnucnet

• Intrinsically 3-d• Easily handles arbitrary nuclear network (bbn to r-

process), including (any number of) isomeric states• Reactions are handled the way humans think about

them: “c12 + he4 o16 + gamma” or “o15 n15 + positron + neutrino_e”

• Hierarchically structured• Naturally uses xml as input (allows for schemas,

stylesheets, xpath selection, etc.)• Read and validate data across the web• Allows for user-supplied screening and NSE correction

factor functions.

Structure of libnucnet

• Libnucnet__Nuc.c/h: a collection of nuclei– Libnucnet__Species: a species– Libnucnet__Nuc: a collection of species

• Libnucnet__Reac.c/h: a collection of nuclear reactions– Libnucnet__Reaction: a reaction– Libnucnet__Reac: a collection of reactions

• Libnucnet.c/h: a network and a collection of zones– Libnucnet__Net: a Libnucnet__Nuc + Libnucnet__Reac– Libnucnet__Zone: a physical zone– Libnucnet: a network plus a collection of zones

XML Data for the nuclear collection<nuclear_data> <!--n--> <nuclide> <z>0</z> <a>1</a> <source>Tuli (2000)</source> <mass>8.071</mass> <spin>0.5</spin> <partf_table> <point> <t9>0.01</t9> <log10_partf>0</log10_partf> </point> <point> <t9>0.15</t9> <log10_partf>0</log10_partf> </point> </partf_table> </nuclide>…</nuclear_data>

XML Data for the nuclear collection (with states)

<!--al26--> <nuclide> <z>13</z> <a>26</a> <states> <state id="g"> <source>Tuli (2000) + Gupta and Meyer (2001)</source> <mass>-12.21</mass> <spin>5</spin> <partf_table> ... </partf_table> </state> <state id="m"> <source>Tuli (2000) + Gupta and Meyer (2001)</source> <mass>-11.982</mass> <spin>0</spin> <partf_table> ,,, </partf_table> </state> </states> </nuclide>

XML Data for Reactions—a rate table

<reaction_data>

<!-- h1 + n to h2 + gamma -->

<reaction> <source>Smith et al. (1993)</source> <reactant>h1</reactant><reactant>n</reactant> <product>h2</product><product>gamma</product> <rate_table> <point> <t9>0.001</t9> <rate>4.6168E+04</rate> <sef>1.000</sef> </point> … </rate_table> </reaction> ….</reaction_data>

XML Data for Reactions—a single rate

<!-- o19 to f19 + electron + anti-neutrino_e -->

<reaction> <source>Nuclear Data tables</source> <reactant>o19</reactant> <product>f19</product> <product>electron</product> <product>anti-neutrino_e</product> <single_rate>1.6251e-01</single_rate></reaction>

XML Data for Reactions—a non-smoker fit

<!– ne15 + n to ne16 + gamma -><reaction> <source>ADNDT (2001) 75, 1 (non-smoker)</source> <reactant>ne15</reactant> <reactant>n</reactant> <product>ne16</product> <product>gamma</product> <non_smoker_fit> <Zt> 10</Zt> <At> 15</At> <Zf> 10</Zf> <Af> 16</Af> <Q> 8.071000</Q> <spint> 0.0000</spint> <spinf> 0.0000</spinf> <TlowHf>-1.0000</TlowHf> <Tlowfit> 0.0100</Tlowfit> <acc> 1.900000e-06</acc> <a1> 6.225343e+00</a1> <a2> 1.023384e-02</a2> <a3>-1.272184e+00</a3> <a4> 3.920127e+00</a4> <a5>-1.966720e-01</a5> <a6> 1.394263e-02</a6> <a7>-1.389816e+00</a7> <a8> 2.983430e+01</a8> </non_smoker_fit></reaction>

Zone data<initial_mass_fractions>

<multiple_zones>

<zone label1="x1" label2="y1" label3="z1"> <nuclide> <z>0</z> <a>1</a> <x>0.5</x> </nuclide> <nuclide> <z>1</z> <a>1</a> <x>0.5</x> </nuclide> </zone> … </multiple_zones></initial_mass_fractions>

Where we’re headed

• Release of libnucnet 0.3 imminent

• Put network code based on libnucnet on line this fall

• My research with libnucnet– Study nuclear network equilibria (NSE, QSE,

etc.)– Build a multi-zone Galactic chemical evolution

network on top of libnucnet.

Four Requirements for Meaningful Measurements for Astrophysics (The et al. 1998)

• An appropriate astrophysical model of events significant for nucleosynthesis . (“Appropriate” does not necessarily = “correct”!)

• An observable from the nucleosynthesis process, usually an abundance result that is either known or measurable.

• The dependency of the value of the observable on the value of a nuclear cross section or other nuclear property.

• An experimental strategy for measuring that cross section, or at least of using measurable data to better calculate it.