Module: Units

This module contains physical constants relevant for nuclear matter and neutron star physics. It also provides functions for converting one type of units into another.

Numerical

Constants for dealing with extreme numerics:

• NUMZERO = 1e-12 (the lowest numerical value allowed)

• NUMINF = 1e30 (the largest numerical value allowed)

• DENSEPSILON = 1e-12 this value is used to renormalize division and avoid dividing but extremely small numbers that cause numerical instabilities

Note

DENSEPSILON is used whenever division by density has to be applied. Those cases usually will give zero in proper analytical limit.

Physical

Note

Physical constants are from NIST website:

• https://physics.nist.gov/cgi-bin/cuu/Value?hbcmevf

• https://physics.nist.gov/cgi-bin/cuu/Value?mnc2mev

• https://physics.nist.gov/cgi-bin/cuu/Value?mpc2mev

Constant	Value	Unit	Description
HBARC	197.3269804	[MeV fm]	\(\hbar c\)
MN	939.5654205	[MeV]	neutron mass \(m_n\)
MP	938.2720882	[MeV]	proton mass \(m_p\)
HBAR2M_n	20.72124837	[MeV*fm \(^2\)]	\(\hbar^2/(2 m_n)\)
HBAR2M_p	20.74981092	[MeV*fm \(^2\)]	\(\hbar^2/(2 m_p)\)
hbar22M0	20.72	[MeV*fm \(^2\)]	rounded \(\hbar^2/(2 m_n)\), used by vsf_NV() and v_NV()

Nucleon masses

The masses of proton, neutron and nucleon (which is their averaged mass). The nucleon mass is an average of proton and neutron mass:

\[m_N=\frac{1}{2} (m_n + m_p) \approx 1.67377585 \cdot 10^{-27}\,\mathrm{kg}. \]

Mass	Value
neutron \(m_n\)	1.6749286 \(\cdot 10^{-27}\) kg
proton \(m_p\)	1.6726231 \(\cdot 10^{-27}\) kg
nucleon \(m_N\)	1.6737759 \(\cdot 10^{-27}\) kg

Neutron star

Some constants are relevant from the point of view of neutron star’s physics. One of them is the neutron drip density \(\rho_{\mathrm{ND}}\) at which excess neutrons are no longer bound to the nuclei and form a superfluid sea. This is how the border between the outer crust and the inner crust is defined. RHOSAT is a rounded value of the nuclear saturation density \(\rho_0\), the density of matter inside heavy nuclei: \(3 \cdot 10^{14}\) g cm ^-3 \(\approx\) 0.179 fm ^-3. The saturation density of a particular functional is somewhat lower (about 0.159 fm ^-3 for BSk31). The crust-core transition takes place at roughly half of \(\rho_0\).

Variable	Density	[g cm -3]	[fm -3]
RHOSAT	\(\rho_0\)	3 \(\cdot 10^{14}\)	0.179
RHOND	\(\rho_{\mathrm{ND}}\)	4 \(\cdot 10^{11}\)	0.00024

List of functions

libnest.units.KtoMev(temp)

Converts temperature \(T\) units from Kelvins to energy \(E\) units in MeVs by setting the Boltzmann constant to 1.

\[E = \frac{k_B}{1\,\mathrm{eV}} 10^{-6} T \approx \frac{T}{11604525006.1598} \]

Parameters:

temp (float) – temperature \(T\) [K]

Returns:

energy \(E\) [MeV]

Return type:

float

See also

MeVtoK()

libnest.units.MeVtoK(energy)

Converts energy \(E\) units in MeVs to temperature \(T\) units from Kelvins by setting the Boltzmann constant to 1.

\[T = \frac{1\,\mathrm{eV}}{k_B} 10^6 E \approx 11604525006.1598 \cdot E \]

Parameters:

energy (float) – energy \(E\) [MeV]

Returns:

temperature \(T\) [K]

Return type:

float

See also

KtoMev()

libnest.units.fm3togcm3(rho)

Function converts density units: fm ^-3 into g cm ^-3. See more here. The numerical factor

\[\frac{m_N}{\mathrm{fm}^3} = 1.67377585 \cdot 10^{15}\frac{\mathrm{g}}{\mathrm{cm}^3} \]

Parameters:

rho (float) – density \(\rho\) [fm ^-3]

Returns:

rho \(\rho\) [g cm ^-3]

Return type:

float

See also

gcm3tofm3()

libnest.units.gcm3tofm3(rho)

Function converts density units: g cm ^-3 into fm ^-3. See more here. The numerical factor

\[\frac{\mathrm{g}}{\mathrm{cm}^3} = \frac{10^{-15}}{1.67377585} \frac{m_N}{\mathrm{fm}^3} \]

Parameters:

rho (float) – density \(\rho\) [g cm ^-3]

Returns:

rho \(\rho\) [fm ^-3]

Return type:

float

See also

fm3togcm3()