17-The nuclear force
All before depends on the nucleons sticking together
Nuclear Force misc
arises from strong force that binds quarks
leakage of strong force
acts like fundamental force
potent, since able to overcome protons
properties
repulsive ~<1fm
attractive at intermediate distances
feeble at a larger distance
plot
need Schrodinger equation
form of potential is important
find depth of potential
find shape of potential
tells us how strong it is
does spin play a role?
This the the N-N which goes into the Schrodinger equation
Deuteron
2H nucleus
simplest nucleus in nature so good to study
so solve Schrodinger eqn for it
General properties
only just a bound state
no excited states, any excitation just disitigrates
low binding energy 2.22 MeV
how binding energy was measured
measure energy released on formation
measure energy required to cause a photo-dissociation
neutron is unstable, but when bound to proton stops being unstable
decay becomes energetically unstable
wavefunction
simplifications
take r as separation between neutron and proton
R diameter of deuteron
V(r) function of r only
assume 1d
assume square well
maths:
wavefunction finite at infinite r and r=0
If nuclear force slightly less deuteron would not exist, and world would not exist
Nuclear Spin
Could be either I=0 or I=1
found to always be 1
therefore NP spins must be parallel
alignment of spins must be important in nuclear potential
known as triplet S state (three projections of S, 1,0 and -1)
therefore the wavefunction needs spin part as well as spatial
Isospin
if only spin and spatial parts included in wavefunction it should asymmetric
describes groups of particles which have nearly the same mass
think of N and P as different states of the same particle
analogous to interinsic spin, but don't get mixed up
each individual nucleon can take on specific values
called third component of t
Arises from strong force independence from elec charge
total isospin is vector sum of individual intrinsic isospins
singlet 0, or triplet, 1
know s=1 so for deuteron choose singlet
because S=0 no n-n or p-p are allowed
operator t
maths: