Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distributions of Long-Lived Radioactive Nuclei Provided by Star Forming
  Environments   Radioactive nuclei play an important role in planetary evolution by providing
an internal heat source, which affects planetary structure and helps facilitate
plate tectonics. A minimum level of nuclear activity is thought to be necessary
--- but not sufficient --- for planets to be habitable. Extending previous work
that focused on short-lived nuclei, this paper considers the delivery of
long-lived radioactive nuclei to circumstellar disks in star forming regions.
Although the long-lived nuclear species are always present, their abundances
can be enhanced through multiple mechanisms. Most stars form in embedded
cluster environments, so that disks can be enriched directly by intercepting
ejecta from supernovae within the birth clusters. In addition, molecular clouds
often provide multiple episodes of star formation, so that nuclear abundances
can accumulate within the cloud; subsequent generations of stars can thus
receive elevated levels of radioactive nuclei through this distributed
enrichment scenario. This paper calculates the distribution of additional
enrichment for $^{40}$K, the most abundant of the long-lived radioactive
nuclei. We find that distributed enrichment is more effective than direct
enrichment. For the latter mechanism, ideal conditions lead to about 1 in 200
solar systems being directly enriched in $^{40}$K at the level inferred for the
early solar nebula (thereby doubling the abundance). For distributed enrichment
from adjacent clusters, about 1 in 80 solar systems are enriched at the same
level. Distributed enrichment over the entire molecular cloud is more
uncertain, but can be even more effective.

10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat