# Source code for galpy.potential.SphericalShellPotential

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#   SphericalShellPotential.py: The gravitational potential of a thin,
#                               spherical shell
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import numpy
from ..util import conversion
from .SphericalPotential import SphericalPotential
[docs]class SphericalShellPotential(SphericalPotential):
"""Class that implements the potential of an infinitesimally-thin, spherical shell

.. math::

\\rho(r) = \\frac{\\mathrm{amp}}{4\pi\,a^2}\\,\\delta(r-a)

with :math:\\mathrm{amp} = GM the mass of the shell.
"""
[docs]    def __init__(self,amp=1.,a=0.75,normalize=False,ro=None,vo=None):
"""
NAME:

__init__

PURPOSE:

initialize a spherical shell potential

INPUT:

amp - mass of the shell (default: 1); can be a Quantity with units of mass or Gxmass

a= (0.75) radius of the shell (can be Quantity)

normalize - if True, normalize such that vc(1.,0.)=1., or, if given as a number, such that the force is this fraction of the force necessary to make vc(1.,0.)=1.; note that because the force is always zero at r < a, this does not work if a > 1

ro=, vo= distance and velocity scales for translation into internal units (default from configuration file)

OUTPUT:

(none)

HISTORY:

2018-08-04 - Written - Bovy (UofT)

2020-03-30 - Re-implemented using SphericalPotential - Bovy (UofT)

"""
SphericalPotential.__init__(self,amp=amp,ro=ro,vo=vo,amp_units='mass')
a= conversion.parse_length(a,ro=self._ro)
self.a= a
self.a2= a**2
if normalize or \
(isinstance(normalize,(int,float)) \
and not isinstance(normalize,bool)):
if self.a > 1.:
raise ValueError('SphericalShellPotential with normalize= for a > 1 is not supported (because the force is always 0 at r=1)')
self.normalize(normalize)
self.hasC= False
self.hasC_dxdv= False

def _revaluate(self,r,t=0.):
"""The potential as a function of r"""
if r <= self.a:
return -1./self.a
else:
return -1./r

def _rforce(self,r,t=0.):
"""The force as a function of r"""
if r <= self.a:
return 0.
else:
return -1/r**2.

def _r2deriv(self,r,t=0.):
"""The second radial derivative as a function of r"""
if r <= self.a:
return 0.
else:
return -2./r**3.

def _rdens(self,r,t=0.):
"""The density as a function of r"""
if r != self.a:
return 0.
else: # pragma: no cover
return numpy.infty

def _surfdens(self,R,z,phi=0.,t=0.):
"""
NAME:
_surfdens
PURPOSE:
evaluate the surface density for this potential
INPUT: