Target detection & normalization

[C.Bauer]

I was not aware of that problem but just found out the following from the manual (p.115 suboption EXPT):

Due to a design limitation in the current version, no target-detection experiment should be normalized to any other experiment, or vice-versa. For normal (not inverse) kinematics it is possible to overcome this restriction by specifying beam detection and giving the equivalent theta_beam range. For inverse kinematics it depends on whether both solutions are detected because of energy thresholds for the scattered particle.

Now I have excactly that case, a MINIBALL experiment, circular CD detector in forward direction (~16-52 degree in LAB-system), inverse kinematics Nd-140 on Ti-48. That means I detect mainly scattered Ti target nuclei on the CD. So I define 2 experiments, differing in scattering angle, and want to normalize one to the other.

When I do that using target detection I can see from the minimization that Gosia cannot do that, the normalization stays 1.0 for both experiments.

So I think I will now pretend projectile detection as suggested, calculate the corresponding angles, of course, but I will just have the higher energy branch of the projectiles corresponding to the detected target particles. How do I take this into account?

Btw, is there maybe some other work-around for that?

[hayes]

Hi Christopher,

Forgive me if I tell you things you already know. Maybe someone will have a more clever solution, but these are my thoughts:

If you have data that include both kinematic solutions, leaving out one of the solutions would almost certainly give a large systematic error in the measured matrix elements, since the Gosia calculations would not match the particle scattering range that was selected to measure the gamma-ray yields. You can get an idea of the magnitude of this error by examining the results of an integration for each kinematic solution.

The main purpose of normalizing one experiment to another is to gain sensitivity to the excitation as a function (usually) of the scattering angle during the fit. But if you have to do this at the expense of some large systematic error, there wouldn't be a benefit.

Are either of the following options open to you?

1. Separate the particle scattering data into two solutions by a particle energy vs. angle gate. This would allow you to write the input so that each of the two kinematic solutions is represented by a different Gosia "experiment." You would have to keep the ends of the projectile scattering range away from the maximum scattering angle so that Gosia won't complain. This approach would allow you to normalize one experiment to another and recover sensitivity in the fit, but you would not have great sensitivity to the lowest E2 matrix elements in the Nd system.
   
2. Use Gosia2 to normalize the gamma-ray yields for Nd to those of 48Ti. The known lifetime or B(E2) (~2% uncertainty) of the Ti 2-->0 transition could be used to fit even the lowest B(E2)s in Nd. Using Gosia2, you would overcome the loss of sensitivity for independently normalized experiments by fitting to the ratio of the Nd and Ti yields, and you would not have to exclude the data near the maximum scattering angle in the sort. The previously measured lifetime or B(E2) would be essential in this method to obtain a unique, meaningful fit.

Let me know if this helps.

Adam

[C.Bauer]

To clarify the problem I should add that I just can see the first 2+ state in Ti-48 as well as Nd-140 excited. The aim of the experiment is to deduce the B(E2) value of Nd-140 (2+1 to 0+1,gs) from a normalization to the excitation of that first excited 2+ state Ti-48.

This is typically a Gosia2 problem I guess, but as I never used that and the matrix elements for Ti-48 are very well known I wanted first to use Gosia with a Ti-48 input file and then give the normalization factors to my Nd-140 input file. That should give me a good result for the Nd-140 excitation except for the fact that I am neglecting the uncertainties in the target excitation of Ti-48 for the moment.

I will report if I am successful with defining projectile angles or have to use Gosia2...

[hayes]

Hi Christopher,

Please do report on your progress. People have used Gosia (1) instead of Gosia2 for these two-state problems with success.

Recently, I decided that a "manual" procedure for calculating the error in the beam-particle matrix element correlated with the errors in the target-particle matrix elements is easier than trying to do it with two Gosia (1) inputs. I plan to write up my proposed method on the Wiki, but remind me if it doesn't come soon enough.

It has been suggested (2008 Gosia Workshop in Warsaw) that the errors in the automated OP,ERRO function in Gosia2 will be underestimated, because they don't include the complete correlations between the two nuclei, and I suspect that this is true. This is the reason that I will suggest a "manual" method for calculating the errors, and the technique is not difficult--it only requires several iterations of a fit for each matrix element's error calculation, which is not much work for two-state problems.

Adam

[C.Bauer]

UPDATE:

I am still using Gosia (1) and I start to get useful results although I still define the target detection angles as it was so in that experiment. I am using the method to run it once for the target with independent normalization and then for the projectile using the normalization constants from the target.

So I have two more questions:

1. Why exactly is Gosia limited that one cannot normalize target detection experiments to each other? I don't see really a reason for that except for the comment in the manual.

2. Dear Adam, have you already made your comment about the new error estimation you mentioned earlier? I found a paragraph in the Wiki but I think you meant something else...

Thank you in advance!

[hayes]

Hi Christopher,

We are not clear on the reason that target-detection experiments must be normalized independently. I have tried to fit normalization constants for target detection to simulated "perfect" data, where the chi-squared value was known to be zero, but I could not find values for these constants that did not give a systematic error in the OP,MINI fit.

(The magnitude of these systematic errors can be estimated by using the output of OP,INTI (or OP,INTG) to generate simulated yield data. It will depend on the scattering angle ranges you use, and you will probably have to hand-fit the proper normalization constants to get chi-squared for the simulated data as close to zero as possible. I think that for a gosia2 problem the normalization of one experiment to another is not usually vital, since each experiment is automatically normalized by gosia2 to the corresponding experiment in the collision-partner's input, so this extra work may not provide much more sensitivity of the matrix elements to the data.)

If you have any success, please let me know.

I put my proposed correlated error procedure on the Wiki here:
http://www-user.pas.rochester.edu/~gosia/mediawiki/index.php/Error_estimation#Brute_force_total_correlated_error_estimation_in_gosia2_problems

I tested this procedure also with simulated data, so that the fit was known to be good, and it gave reasonable correlated error estimates that seemed to reflect the error bars that were put on the simulated data. If you have anything to add to the Wiki on this topic, please feel free.


Best,
Adam