GOSIAAs 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

YIELDGOSIA 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 mg/cm2

88Kr simulation – level layout

88Kr simulation – level layout

One usually adds some „buffer” states on top of observed ones to avoid artificial population build-up it the highest observed state

4

3

2

1

5

6

megengeneration 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.

megengeneration of matrix elements set

parity

level number

spin

level energy[MeV]

input termination

 iwanicki@buka:~/Coulex/88Kr$ megen 1 Create setup for this multipolarity (y/n)n 2Create setup for this multipolarity (y/n)y Do you want them coupled ?n Please give limit value-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

megengeneration of matrix elements set

E2

M1

How to get matrix elementsfor 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,THEOgeneration 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 for 88KrOP,THEO20,41,2,3,42,25,621,10.3,0,01,20.05,0,00,07 1,20.05,0,00,00

number of bands (2)First band, K and number of statesband member indicesSecond band, K and number of statesMultipolarity E2Bands 1 and 1 (in-band)Moment Q1 of the rotational band

Multipolarity M1

4

3

2

1

5

6

band 1 band 2

end of band-band input

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 for integration:

• One has to find projectile energy Emin at the end of the target to know the energy range for integration.

dE

dxdEYYdx

thickness E

E 0

min

max

1

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...

y2c code

Aeffppscurrentyield ][106.7 6

Count Rate =

yield count rate

target

Having the yields calculated...

• Kasia is going to show the way to estimate experimental errors of matrix elements to be measured:

GOSIA

spectroscopicdata

generatedyields GOSIA

matrix elementerrors estimate

“Saturation” of the yield