Difference between revisions of "DU Run"

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[[File:theta_view2.png]]
 
[[File:theta_view2.png]]
  
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Dot product of two vectors <math>(a,b)=|a| \cdot |b| \cdot cos\theta </math>
+
The dot product of two vectors <math>\vec a \cdot \vec b=|\vec a|  |\vec b| cos\theta </math>, <math>\vec a = a_x \hat{x} + a_y \hat{y} + a_z \hat{z}</math> and <math>\vec b = b_x \hat{x} + b_y \hat{y} + b_z \hat{z}</math>.
  
−
For instance, for the case <math>x1>37.5</math> and <math>x2<37.5</math> the angle is <math>theta2 = acos( \frac{l1 \cdot l2-(x1-37.5) \cdot (37.5-x2)}{\sqrt{l1^2+(x1-37.5)^2} \cdot \sqrt{l2^2+(37.5-x2)^2}} )</math>
+
For instance, for the case <math>x1>37.5</math> and <math>x2<37.5</math> the angle is <math>theta2 = acos( \frac{l1 \cdot l2-(x1-37.5) \cdot (37.5-x2)}{\sqrt{l1^2+(x1-37.5)^2} \cdot \sqrt{l2^2+(37.5-x2)^2}} )</math>, where 37.5 cm is the x-middle coordinate (the reference point of the coordinate system), the x-zero is at the bottom and x-top is 75 cm is the active area size.
  
 
The target was considered to be the point. There was no resolution along y-coordinate of the hit of each detector. All hits were assumed to hit the y-center of each detector.
 
The target was considered to be the point. There was no resolution along y-coordinate of the hit of each detector. All hits were assumed to hit the y-center of each detector.
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The X-coordinate of the neutron hit of each detector was determined from the TDC difference spectra with application of real calibration factors obtained in separate experiment with Co-60 source. As an example of the cuts applied see the plot below:
 
The X-coordinate of the neutron hit of each detector was determined from the TDC difference spectra with application of real calibration factors obtained in separate experiment with Co-60 source. As an example of the cuts applied see the plot below:
  
−
[[File:DetM_Calibr_data_mis.png | 300 px]]
+
[[File:DetM_Calibr_data_mis.png | 500 px]]
  
 
The data from the current run 4118 are plotted below:
 
The data from the current run 4118 are plotted below:
  
 
[[File:r4118_tdc_diff.png]]
 
[[File:r4118_tdc_diff.png]]
 +
 +
And the same data on the linear scale:
 +
 +
[[File:r4118_tdc_diff_linscale.png]]
  
 
The timing cuts were applied for TDC sum spectra. It should be noticed that time cuts included both neutron and photon areas because in four fold coincidences the photon accidentals will dissappear.
 
The timing cuts were applied for TDC sum spectra. It should be noticed that time cuts included both neutron and photon areas because in four fold coincidences the photon accidentals will dissappear.
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[[File:r4118_tdc_single.png]]
 
[[File:r4118_tdc_single.png]]
 +
 +
If we make 4x coincidences between the detectors with the timing cut on the neutron region only (no conditions applied on the x-ccordinate hit), we'll get
 +
 +
[[File:TDC_4xcoinc_nArea.png]]
 +
 +
The total number of coincidences is 31.
 +
 +
If we make 4x coincidences between the detectors with the timing cut on the neutron and photon regions (no conditions applied on the x-ccordinate hit), we'll get
 +
 +
[[File:TDC_4xcoinc_gnArea2.png]]
 +
 +
The total number of coincidences is 4371.
 +
 +
neutron_angle_phi.png
 +
The data bank was created for single run and file looked like the one on the picture below:
 +
 +
[[File:Data_bank_img.png | 800 px]]
 +
 +
The first column of data obtained for each detector is the event number and the second one is the x-coordinate of neutron hit.
 +
 +
After processing of the main data bank the 2n coincidences were extracted for each possible detector hit combinations. The example of the data file for 2n coincidences of Det F and Det G is presented below:
 +
 +
[[File:Coincidence_data_pic.png]]
  
 
After writing a bunch of scripts the root file was created and the data are plotted below:
 
After writing a bunch of scripts the root file was created and the data are plotted below:
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The uncertainties on the <math>\theta</math> angle are determined by the width of the TDC difference spectra. Should be discussed.
 
The uncertainties on the <math>\theta</math> angle are determined by the width of the TDC difference spectra. Should be discussed.
 +
 +
==2n opening angle after taking into account the z-coordinate==
 +
 +
The 2n opening angle after taking in th account the z-coordinate of the vertex and timing cuts including both neutron area and photon region:
 +
 +
[[File:2n_opening_angle_zcomp_gnArea.png]]
 +
 +
The 2n opening angle after taking in th account the z-coordinate of the vertex and timing cuts including neutron region only:
 +
 +
[[File:2n_opening_angle_zcomp_nArea2.png]]
 +
 +
==Simulation of neutron angular distribution after the deuteron photodisintegration==
 +
Spherical coordinates [Weisstein, Eric W. "Spherical Coordinates." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SphericalCoordinates.html ]:
 +
 +
[[File:Sperical_coordinates_plot.gif]]
 +
 +
The simulation of neutron angular distribution has been done using D2 sphere of diameter 6 cm and monoenergetic 5 MeV photn beam (<math>10^6</math> photons) going along the z-axis. The neutrons were observed outside of the sphere. The physics for neutron interaction with the matter was off to prevent the material of the target to obscure the angular distribution. Physics of photonuclear reactions was on.
 +
 +
In these coordinates the neutron angular distribution looks like:
 +
 +
[[File:neutron_angle_phi.png]]
 +
 +
[[File:neutron_angle_theta.png]]
 +
 +
According to
 +
 +
[[File:Cutout2.png]]
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 +
[[File:cutout.png]]
 +
 +
<math>\frac{\sigma_m}{\sigma_e} = 0.61 \pm 0.04</math>, hence, <math>\frac{a}{b} = 0.41 \pm 0.04</math>
 +
 +
So the <math>\phi</math> distribution of neutrons (in the coordinate system described above) should look like:
 +
 +
[[File:theory_neut_distr.png | 400 px]]

Latest revision as of 17:11, 2 November 2012

Angular dependence [math](\theta,\phi)[/math] of two neutrons emitted from DU target was determined.

The [math]\theta[/math] angle was measured as shown below in the picture:

Theta view2.png

The dot product of two vectors [math]\vec a \cdot \vec b=|\vec a| |\vec b| cos\theta [/math], [math]\vec a = a_x \hat{x} + a_y \hat{y} + a_z \hat{z}[/math] and [math]\vec b = b_x \hat{x} + b_y \hat{y} + b_z \hat{z}[/math].

For instance, for the case [math]x1\gt 37.5[/math] and [math]x2\lt 37.5[/math] the angle is [math]theta2 = acos( \frac{l1 \cdot l2-(x1-37.5) \cdot (37.5-x2)}{\sqrt{l1^2+(x1-37.5)^2} \cdot \sqrt{l2^2+(37.5-x2)^2}} )[/math], where 37.5 cm is the x-middle coordinate (the reference point of the coordinate system), the x-zero is at the bottom and x-top is 75 cm is the active area size.

The target was considered to be the point. There was no resolution along y-coordinate of the hit of each detector. All hits were assumed to hit the y-center of each detector.

The [math]\phi[/math] angle was measured as shown below in the picture:

Phi view.png

The X-coordinate of the neutron hit of each detector was determined from the TDC difference spectra with application of real calibration factors obtained in separate experiment with Co-60 source. As an example of the cuts applied see the plot below:

DetM Calibr data mis.png

The data from the current run 4118 are plotted below:

R4118 tdc diff.png

And the same data on the linear scale:

R4118 tdc diff linscale.png

The timing cuts were applied for TDC sum spectra. It should be noticed that time cuts included both neutron and photon areas because in four fold coincidences the photon accidentals will dissappear.

R4118 tdc sum.png

In the case of Det K it was hard to observe the neutron area and the TDC singles spectra were used to set the time cut (see Det K data on the plot below):

R4118 tdc single.png

If we make 4x coincidences between the detectors with the timing cut on the neutron region only (no conditions applied on the x-ccordinate hit), we'll get

TDC 4xcoinc nArea.png

The total number of coincidences is 31.

If we make 4x coincidences between the detectors with the timing cut on the neutron and photon regions (no conditions applied on the x-ccordinate hit), we'll get

TDC 4xcoinc gnArea2.png

The total number of coincidences is 4371.

neutron_angle_phi.png The data bank was created for single run and file looked like the one on the picture below:

Data bank img.png

The first column of data obtained for each detector is the event number and the second one is the x-coordinate of neutron hit.

After processing of the main data bank the 2n coincidences were extracted for each possible detector hit combinations. The example of the data file for 2n coincidences of Det F and Det G is presented below:

Coincidence data pic.png

After writing a bunch of scripts the root file was created and the data are plotted below:

R4118 3D corr plot.png

In order to see better [math]\theta[/math] and [math]\phi[/math] distributions it was created a couple of plots with corresponding projections:

[math]\theta[/math] projection of the 3D plot

R4118 theta proj.png

[math]\phi[/math] projection of the 3D plot

R4118 phi proj.png

The uncertainties on the [math]\phi[/math] angle are determined by the width of the neutron detectors and the distance from the target.

The uncertainties on the [math]\theta[/math] angle are determined by the width of the TDC difference spectra. Should be discussed.

2n opening angle after taking into account the z-coordinate

The 2n opening angle after taking in th account the z-coordinate of the vertex and timing cuts including both neutron area and photon region:

2n opening angle zcomp gnArea.png

The 2n opening angle after taking in th account the z-coordinate of the vertex and timing cuts including neutron region only:

2n opening angle zcomp nArea2.png

Simulation of neutron angular distribution after the deuteron photodisintegration

Spherical coordinates [Weisstein, Eric W. "Spherical Coordinates." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SphericalCoordinates.html ]:

Sperical coordinates plot.gif

The simulation of neutron angular distribution has been done using D2 sphere of diameter 6 cm and monoenergetic 5 MeV photn beam ([math]10^6[/math] photons) going along the z-axis. The neutrons were observed outside of the sphere. The physics for neutron interaction with the matter was off to prevent the material of the target to obscure the angular distribution. Physics of photonuclear reactions was on.

In these coordinates the neutron angular distribution looks like:

Neutron angle phi.png

Neutron angle theta.png

According to

Cutout2.png

Cutout.png

[math]\frac{\sigma_m}{\sigma_e} = 0.61 \pm 0.04[/math], hence, [math]\frac{a}{b} = 0.41 \pm 0.04[/math]

So the [math]\phi[/math] distribution of neutrons (in the coordinate system described above) should look like:

Theory neut distr.png

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