# Re: RE: RE: [SPAM] RE: [SPAM] RE: [fluka-discuss]: Angular distribution of usryield

From: YANG Tao <yangt_at_ihep.ac.cn>
Date: Thu, 25 Oct 2018 17:11:29 +0800 (GMT+08:00)

Dear Vasilis,

Tanks for reply. Isn't this relation (Ω[i+1] - Ω[i]) /(θ[i+1]-θ[i]) =2πsin((θ[i]+θ[i+1])/2) true when Δθ->0 ? As long as we calculate Ω[i] as 2π(1-cosθ[i]), what's the difference of the expression of (Ω[i+1] - Ω[i]) /(θ[i+1]-θ[i]) and 2πsin((θ[i]+θ[i+1])/2)? I calculate them and find the difference can be ignored if (θ[i+1]-θ[i]) is rather small. Since scoring intervals are in polar angle, the mean value is naturally for angle θ, why is the mean in Ω?

Best regards!

Yang.

-----原始邮件-----

1) Due to the cos() you will get a minus in the ΔΩ/Δθ so I've inverted one of the terms to make it positive
2) Making the conversion discrete instead of differentials you avoid the problem of the mean and it is the correct
way as the histogram works. In the histogram you don't score dN/dΩ but rather ΔΝι/ΔΩι.
Finally what is the mean? why the mean in θ and not the mean in Ω, what is more correct?
3) Correct
V.

From: YANG Tao [yangt_at_ihep.ac.cn]
Sent: Wednesday, October 24, 2018 18:08
To: Vasilis Vlachoudis
Cc: fluka-discuss_at_fluka.org
Subject: Re: RE: [SPAM] RE: [SPAM] RE: [fluka-discuss]: Angular distribution of usryield

Dear Vasilis,

Thanks for your interpretation.unfortunately, I still have some questions, maybe I have some misunderstanding of the concrete calculation procedure.

(1) Do you mean like this "dN/dθ=(3rd column of ***tab.lis file)* (Ω[i+1] - Ω[i]) /(θ[i]-θ[i+1])(?isn't it θ[i+1]-θ[i]?)"? I guess θ[i] and θ[i+1] is the 1st and 2nd column of the ***tab.lis file, isn't it?

(2) (Ω[i+1] - Ω[i]) /(θ[i+1]-θ[i])->2πsinθ[i] whenΔθ->0,I really don't know why you calculate it by this method? Is directly calculation as "dN/dθ=(3rd column of tab.lis file)* 2πsin((θ[i]+θ[i+1])/2) "(i.e. the mean value of θ[i] and θ[i+1] ) not correct?

(3) In addition,If θ[i],θ[i+1] is correspondly the 1st and 2nd column of the output file (***tab.lis), how to obtain Ω[i+1],Ω[i] (this value is not the direct output value)? Does calculate Ω[i] like "Ω[i]=2π(1-cosθ[i])"?

Best regards

Yang

-----原始邮件-----

Sorry for before, I mistyped "shape" were I wanted to say "physical meaning" of the distribution.
the shape=the way of representing which as I said changes with the change of variable, but the
physical meaning always remains the same independent of our math representation.

The definition of the solid angle is dΩ = sinθ dθ dφ, and once you integrate over φ you get
your formula dΩ = 2π sinθ dθ, which has nothing to do with any distribution.
Internally the USRYIELD is scored as weighted with 1/(2π sinθ) so directly in solid angle.

The problem lies on what you consider as θ of each bin in the histogram.
For me the best way would be to multiply by width of each bin in solid
angle ΔΩ[i]=Ω[i+1] - Ω[i] and divide it by the width in angle Δθ[i]=θ[i]-θ[i+1], which
should tend to be equal to sinθ for Δθ->0 but at least it will take into account the effect
of the variable bin-size.

Vasilis

From: YANG Tao [yangt_at_ihep.ac.cn]
Sent: Wednesday, October 24, 2018 13:50
To: Vasilis Vlachoudis
Cc: fluka-discuss_at_fluka.org
Subject: Re: [SPAM] RE: [SPAM] RE: [fluka-discuss]: Angular distribution of usryield

Dear Vasilis,

Thanks for your patient interpretation.As you say, when I want to get dN/dθ, does it mean the only thing I would do is to multiply the output results(the 3rd column of ***tab.lis,i.e., dN/dΩ) with 2πsinθ? Besides, is the relation dΩ=2πsinθdθ (or Ω=2π(1-cosθ) always true in any condition especially the nonuniform distribution condition? If it is not always true, how to obtain the relation of dΩ and dθ?

Best regards!

Yang

-----原始邮件-----

Hi Yang,

1) The conversion from dΩ to dθ is just a mathematical conversion and does not imply anything on the shape of
the distribution, just a different way of presenting it. Of course in the scoring we are not dealing with differentials (dθ)
but rather discrete intervals (Δθ), which the width choice must be done under the assumption that Δθ is close to zero
2) You are right, the scoring intervals are in angle however according to Note 5 your end result is per steradian
inside this angular interval.

Vasilis
From: YANG Tao [yangt_at_ihep.ac.cn]
Sent: Monday, October 22, 2018 17:56
To: Vasilis Vlachoudis
Cc: fluka-discuss_at_fluka.org
Subject: Re: [SPAM] RE: [fluka-discuss]: Angular distribution of usryield

Dear Vasilis,

Thanks for your reply. The second question in my last email now is clear to me under your interpretation. But to the 1st question,I am still puzzled.

(1)I multiply the factor 2πsinθ with dθ to get dΩ, but which is based on the assumption of a isotropic distribution, however, this is a transcendental method, how can we know in advance the distribution is isotropic? Or dΩ=2πsinθdθ is only a geometric factor, the actual distribution is already calculated in the dN/dΩ, so to obtain dN/dθ we only just multiply the factor 2πsinθ with the output of fluka usryield card with an angular scoring?

(2)Another puzzled thing is that the distribution is given in steradian, but when I look at the output of the "gem_32_tab.lis" , the 1st column is from 0 to π(shown in attachment), which is still likely expressed in θ as I set in the input file, but the yield is referred to solid angle. As we all know , Ω will vary from 0 to 4π if θ from 0 to π (Ω=2π(1-cosθ)), why the output presents a maximum of π? If the 1st column is still θ, why can we get a flat curve like a isotropic distribution and why can we say the variable is Ω ?

Best regards!
Yang

-----原始邮件-----

Hi Yang,

1. indeed as note 6 of USRYIELD states the results are always per steradian if an angular scoring is used. To obtain the dN/dtheta you have to calculate
the dtheta/domega when you know that the omega = 2pi(1-cos(theta))
2. As the header of the sum.lis is stating the total response is integrated over x1 (and not x2) you need to multiply with the dx2 to get the similar result
as in the usrbdx 0.2155*2e-3 ~= 4.3e-4

Cheers
Vasilis
From: owner-fluka-discuss_at_mi.infn.it [owner-fluka-discuss_at_mi.infn.it] on behalf of YANG Tao [yangt_at_ihep.ac.cn]
Sent: Sunday, October 21, 2018 04:04
To: fluka-discuss_at_fluka.org
Subject: [fluka-discuss]: Angular distribution of usryield

Dear fluka users,

Recently I simulate the angular distribution of secondary ions from (n,B) reaction, I using USRYIELD card to obtain this. However, I cannot interpret the results.

� I set the first quantity polar angle θ (polar angle in the c.m.s. frame, relative to the primary beam direction)and second E, I get a similar isotropic distribution over the polar θ,indeed, I know this distribution is isotropic, but it corresponds to the solid angle Ω not the polar angle θ(i.e.,dΩ=2πsinθdθ). Suppose dN/dΩ=A(some constant),thus,dN/dθ=2Aπsinθ,so at the angle near 0° , we should get a minimal value, and get a maximal value near 90° (I think it is some counterintuitive). Maybe I misunderstand the output of USRYIELD card, so could anyone interpret the meaning of USRYIELD setting. I read the manual, it states:

"In the case of polar angle quantities (| ie| or | ia| = 14, 15, 17, 18, 24, 25) the differential yield is always referred to solid angle in steradian, although input is specified in radian or degrees."

Does it mean the results shown in figure1 is only dN/dΩ? I'm very confused about this, if it is the result of dN/dΩ, then how to obtain dN/dθ (the strange thing is that I set the SDUM as polar angle in the usryield input, now that it cannot give the polar angle distribution, why the sdum says it were polar angle)? I try to get dN/dθ only by multiplying the USRYIELD output results by the factor 2πsinθ (shown in figure2, indeed showing a minimal near 0°), which I think maybe not the correct method since we will loss the statistical meaning if we priori assume the distribution is isotropic in solid angle Ω.

� Besides, I find the total response of 32BIN unit of the input file is 0.2155161(gem_32_sum.lis), which I think is the total yield of α particle leaving from the layer since it is integrated over two quantities, but the value doesn't match the total response of 25BIN((gem_25_sum.lis)) result which is 4.3065209E-04(gem_25_sum.lis,this value seems to be the true yield basing on the reaction cross section ), do the two responding values have different meaning?

Any help is appreciate!

Best regards!

Yang

```--

E-mail：yangt_at_ihep.ac.cn

You can manage unsubscription from this mailing list at https://www.fluka.org/fluka.php?id=acc_info
```
Received on Thu Oct 25 2018 - 12:35:30 CEST

This archive was generated by hypermail 2.3.0 : Thu Oct 25 2018 - 13:22:02 CEST