Transcript GOSIA - Uniwersytet Warszawski

GOSIA
As a Simulation Tool
J.Iwanicki,
Heavy Ion Laboratory, UW
OUTLINE
Our goal is to estimate gamma yieds
• What the yield is
– Point Yield vs. Integrated Yield
• What they are needed for
• What is needed to calculate it
– Definition of the nucleus considered
– Definition of the experiment
YIELD
GOSIA recognizes two types of yields:
• Point yields calculated for:
– Excited levels layout
– Collision partner
– Matrix element values
– CHOSEN particle energy and scattering
angle
• Integrated yields calculated for:
– (... as above but ...)
– A RANGE of scattering angles and energies
POINT YIELD
How GOSIA does it?
• Assumes nucleus properties and collision partner;
• starts with experimental conditions (angle,
energy) and matrix element set
• solves differential equations to find level
populations;
• calculates deexcitation using gamma detection
geometry, angular distributions, deorientation and
internal conversion into acount.
POINT YIELD
Point yields:
• are fast to be calculated...
• ...so they are used at minimisation stage
• OP,POIN – if one needs a quick look
• but are good for one energy and
one (particle scattering) angle
INTEGRATED YIELD
Integrated yields
• are something close to reality
• but quite slow to calculate
Useful integration options:
• axial symmetry option
• circular detector option
• PIN detector option (multiple particle detectors)
YIELD
• GOSIA calculates yields as differential
cross sections, integrated over in-target
particle energies and particle scattering
angles
– ‘differential’ in  but integrated for particles
• The ‘GOSIA yield’ may be understood as a
mean differential cross section multiplied
by target thickness (in mg/cm2)
[Y]=mb/sr 
2
mg/cm
88Kr
simulation – level layout
88Kr
simulation – level layout
4
5
3
6
2
1
One usually adds some „buffer” states on top
of observed ones to avoid artificial population
build-up it the highest observed state
megen
generation of matrix elements set
Apply  transition selection rules to create a
set of all possible matrix elements involved
in excitation.
• This is easy but takes time and any error will
corrupt the results of simulation!
• Tomek quickly wrote a simple code to do the
job which uses data in GOSIA format.
megen
level
number
generation of matrix elements set
parity
spin
level
energy
[MeV]
input termination
megen
generation of matrix elements set
iwanicki@buka:~/Coulex/88Kr$ megen
1
Create setup for this multipolarity (y/n)
n
2
Create setup for this multipolarity (y/n)
y
Do you want them coupled ?
n
Please give limit value
E2
-1.5 1.5
3
Create setup for this multipolarity (y/n)
n
(…)
7
Create setup for this multipolarity (y/n)
y
Do you want them coupled ?
n
Please give limit value
-1 1
8
Create setup for this multipolarity (y/n)
n
M1
How to get matrix elements
for simulation from?
• Check the literature for published values
• Get all the available spectroscopic data
(lifetimes, E2/M1 mixing ratios, branching ratios)
• Ask a theoretician
• Use OP,THEO to generate the rest from
rotational model
• Do some fitting with spectroscopic data only
OP,THEO
generation of a starting point
From the GOSIA manual:
• OP, THEO generates only the matrix specified
in the ME input and writes them to the (...) file.
• For in-band or equal-K interband transitions
only one (moment) marked Q1 is relevant. For
non-equal K values generally two moments
with the projections equal to the sum and
difference of K’s are required (Q1 and Q2),
unless one of the K’s is zero, when again only
Q1 is needed.
• For the K-forbidden transitions a three
parameter Mikhailov formula is used.
OP,THEO
88
2
0,4
number of bands (2)
1,2,3,4
First band, K and number of states
2,2
band member indices
5,6
Second band, K and number of states
2
Multipolarity E2
1,1
Bands 1 and 1 (in-band)
0.3,0,0
Moment Q1 of the rotational band
1,2
0.05,0,0
Multipolarity M1
band 1
band 2
0,0
4
5
7
1,2
3
6
0.05,0,0
2
end of band-band
0,0
input
0
1
OP,THEO for Kr
end of
multipolarities loop
Minimisation with OP,MINI
• Some minimisation would be in order but
minimisation itself is a bit complex subject...
• Let’s assume we have some best possible
Matrix Elements set.
• Next step is the integration over particle
energy and angle.
Integration with OP,INTG
Few hints:
• READ THE MANUAL, it is not easy!
• Integration over angles: assume axial
symmetry if possible (suboption of EXPT)
• Theta and energy meshpoints have to be
given manually, do it right or GOSIA will
go astray!
Integration with OP,INTG
• Yield integration over energies: stopping
power used to replace thickness with energy
E min
for integration: thickness
1
0 Ydx  E max
 Y dE dE
dx
• One has to find projectile energy Emin at the
end of the target to know the energy range
for integration.
YIELD  COUNT RATE
• GOSIA is aware of gamma detectors set-up
• Gamma yield depends on detector angle (angular
distribution)
• However, angular distributions are flattened by
detection geometry (both for particle and gamma )
• Gamma detector geometry is calculated at the
initial stage (geometry correction factors are
calculated and stored for yield calculation)
YIELD  COUNT RATE
• One may try to reproduce gamma detector
set-up of the intended experiment
• or assume the symmetry of the detection
array and calculate everything with a virtual
gamma detector covering 2 of the full
space (huge radius, small distance to target)
YIELD  COUNT RATE
• Taking into account the solid angle,
Avogadro number, barns etc, beam current,
total efficiency...
6
7.6 10  yield  current[ pps]  eff
Count Rate =
Atarget
yield  y2c code  count rate
Having the yields calculated...
• Kasia is going to show the way to estimate
experimental errors of matrix elements to be
measured:
spectroscopic
data
GOSIA
generated
yields
GOSIA
matrix element
errors estimate
“Saturation” of the yield