## Physics.TimeDilationMeasurementsWithFastIonsAt34PercentCAtGSI History

October 10, 2010, at 08:53 PM by 91.67.138.141 -
Changed lines 80-81 from:

Example for a saturation signal with Li ions at 6.4%c
to:

Example for a saturation signal with Li ions at 6.4%c
October 10, 2010, at 08:51 PM by 91.67.138.141 -
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http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ion 7Li+

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ion 7Li+

Changed lines 77-79 from:

Setup ESR experiment for beamtime August 2007
to:

Setup ESR experiment for beamtime August 2007

Example for a saturation signal with Li ions at 6.4%c
May 13, 2010, at 12:32 PM by 91.67.139.210 -
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<param name="movie" value="outwmv2.swf"/>

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<param name="movie" value="http://www.sascha-reinhardt.de/pmwiki/uploads/outwmv2.swf"/>

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<embed src="outwmv2.swf" menu="false" quality="high" bgcolor="#FFFFFF" width="320" height="240" name="player" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer"/>

to:

<embed src="http://www.sascha-reinhardt.de/pmwiki/uploads/outwmv2.swf" menu="false" quality="high" bgcolor="#FFFFFF" width="320" height="240" name="player" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer"/>

May 13, 2010, at 12:29 PM by 91.67.139.210 -
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to:

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<noscript><a href=http://www.dvdvideosoft.com/guides/avs/burn-video-files-to-DVD.htm>burn dvd</a></noscript> <embed src="http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/player.swf?file=http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/gsi_ani.flv&size=false&aplay=false&autorew=false&title=" menu="false" quality="high" bgcolor="#FFFFFF" width="320" height="270" name="player" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer"/>

to:

<noscript><a href="http://www.dvdvideosoft.com/products/dvd/Free-YouTube-to-MP3-Converter.htm">mp3 download</a></noscript> <embed src="outwmv2.swf" menu="false" quality="high" bgcolor="#FFFFFF" width="320" height="240" name="player" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer"/> </object>

May 31, 2009, at 08:49 AM by 94.216.205.149 -
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May 31, 2009, at 08:48 AM by 94.216.205.149 -
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May 31, 2009, at 08:48 AM by 94.216.205.149 -
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May 31, 2009, at 08:47 AM by 94.216.205.149 -
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February 13, 2009, at 03:07 PM by 140.181.11.236 -
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## Time dilation experiment at 34%c using laser spectroscopy

February 13, 2009, at 03:05 PM by 140.181.11.236 -
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July 19, 2008, at 10:12 PM by 92.74.114.2 -
Changed line 60 from:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ion 7Li+

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ion 7Li+

July 19, 2008, at 10:11 PM by 92.74.114.2 -
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// //

to:
July 19, 2008, at 10:11 PM by 92.74.114.2 -
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Setup ESR experiment for beamtime August 2007
to:

Setup ESR experiment for beamtime August 2007

// //

July 19, 2008, at 10:10 PM by 92.74.114.2 -
Changed line 60 from:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ion 7Li+

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ion 7Li+

July 19, 2008, at 10:10 PM by 92.74.114.2 -
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to:

Setup ESR experiment for beamtime August 2007
July 19, 2008, at 10:08 PM by 92.74.114.2 -
Changed lines 63-65 from:
to:
July 19, 2008, at 10:06 PM by 92.74.114.2 -
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July 19, 2008, at 10:00 PM by 92.74.114.2 -
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http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions To excite this transition the parallel laser has wavelength of 386 nm and the antiparallel laser has a wavelength of 780 nm. The antiparallel laser can be realized by a laser diode and the parallel laser by a frequency doubled of a titanium sapphire laser. The overlap between the laser beams and the ion beam is done by mechanical apperaturs and the fluorescens is detected by photomultipliers distributed over the interaction region.

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ion 7Li+ To excite this transition the parallel laser has wavelength of 386 nm and the antiparallel laser has a wavelength of 780 nm. The antiparallel laser can be realized by a laser diode and the parallel laser by a frequency doubled of a titanium sapphire laser. The overlap between the laser beams and the ion beam is done by mechanical apperaturs and the fluorescens is detected by photomultipliers distributed over the interaction region.

July 02, 2008, at 12:20 PM by 130.183.91.199 -
Changed lines 42-43 from:
\nu_0=(546\ 466\ 918\ 531\pm 73)
kHz.
to:
\nu_0=(546\ 466\ 918\ 531\pm 73)\mbox{ kHz.}
July 02, 2008, at 12:19 PM by 130.183.91.199 -
Changed lines 42-43 from:
\nu_0=546\ 466\ 918\ 531\pm 73) kHz
.
to:
\nu_0=(546\ 466\ 918\ 531\pm 73)
kHz.
June 28, 2008, at 09:36 PM by 92.74.122.26 -
Changed line 60 from:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

June 28, 2008, at 09:35 PM by 92.74.122.26 -
Changed line 60 from:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

June 28, 2008, at 09:35 PM by 92.74.122.26 -
Changed line 60 from:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

June 28, 2008, at 09:28 PM by 92.74.122.26 -
Changed lines 36-37 from:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent speed of light were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm. The results are published in (SaschaReinhardtNaturePhysics2007):

to:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent speed of light were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm. An complete describtion of the experiment is given in the PhD thesis of Sascha Reinhardt. The final results are published in (SaschaReinhardtNaturePhysics2007):

June 28, 2008, at 09:25 PM by 92.74.122.26 -
Changed line 60 from:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

June 28, 2008, at 09:25 PM by 92.74.122.26 -
Changed line 60 from:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

to:

http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions

June 28, 2008, at 09:22 PM by 92.74.122.26 -
Changed lines 59-61 from:

For the laser spectroscopy at ESR the \Lambda-system of the lithium ion is used. To excite this transition the parallel laser has wavelength of 386 nm and the antiparallel laser has a wavelength of 780 nm. The antiparallel laser can be realized by a laser diode and the parallel laser by a frequency doubled of a titanium sapphire laser. The overlap between the laser beams and the ion beam is done by mechanical apperaturs and the fluorescens is detected by photomultipliers distributed over the interaction region.

to:

For the laser spectroscopy at ESR the \Lambda-system of the lithium ion is used. http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/TIME_lithiumschema.png | Energy level of lithium ions To excite this transition the parallel laser has wavelength of 386 nm and the antiparallel laser has a wavelength of 780 nm. The antiparallel laser can be realized by a laser diode and the parallel laser by a frequency doubled of a titanium sapphire laser. The overlap between the laser beams and the ion beam is done by mechanical apperaturs and the fluorescens is detected by photomultipliers distributed over the interaction region.

June 28, 2008, at 06:04 PM by 92.74.122.26 -
Changed line 59 from:
to:

For the laser spectroscopy at ESR the \Lambda-system of the lithium ion is used. To excite this transition the parallel laser has wavelength of 386 nm and the antiparallel laser has a wavelength of 780 nm. The antiparallel laser can be realized by a laser diode and the parallel laser by a frequency doubled of a titanium sapphire laser. The overlap between the laser beams and the ion beam is done by mechanical apperaturs and the fluorescens is detected by photomultipliers distributed over the interaction region.

June 28, 2008, at 01:37 AM by 92.75.9.198 -
Changed line 9 from:

There are many open questions in the description of nature like how to combine gravity and quantum mechanics or what is dark matter/dark energy. Also CPT-symmetry and Lorentz-Transformation are under investigation if they are correct. In the following an experiment at GSI is presented as a continuation of a former experiment at MPI for nuclear physics which delivers one of the best test of Lorentz violation. At the experimental storage ring ESR lithium ions are accelerated to a velocity of 34% speed of light and laser spectroscopic methods are used to measure the time dilation and compare it with theory of Special Relativity (SR).

to:

There are many open questions in the description of nature like how to combine gravity and quantum mechanics or what is dark matter/dark energy. Also CPT-symmetry and Lorentz-Transformation are under investigation if they are correct. In the following an experiment at GSI is presented as a continuation of a former experiment at MPI for nuclear physics which delivers one of the best test of Lorentz violation. At the experimental storage ring ESR lithium ions are accelerated to a velocity of 34% speed of light and laser spectroscopic methods are used to measure the time dilation and compare it with theory of Special Relativity (SR).

June 28, 2008, at 01:35 AM by 92.75.9.198 -
Changed lines 31-32 from:

For comparision of different experiments and the last relation can be written as (s. Testtheories)

to:

For comparision of different experiments the last relation can be written as (s. Testtheories)

June 28, 2008, at 01:33 AM by 92.75.9.198 -
Changed line 9 from:

There are many open questions in the description of nature like how to combine gravity and quantum mechanics or what is dark matter/dark energy. Also CPT-symmetry and Lorentz-Transformation are under investigation if they are correct. In the following an experiment at GSI is presented as a continuation of a former experiment at MPI for nuclear physics which delivers one of the best test of Lorentz violation.

to:

There are many open questions in the description of nature like how to combine gravity and quantum mechanics or what is dark matter/dark energy. Also CPT-symmetry and Lorentz-Transformation are under investigation if they are correct. In the following an experiment at GSI is presented as a continuation of a former experiment at MPI for nuclear physics which delivers one of the best test of Lorentz violation. At the experimental storage ring ESR lithium ions are accelerated to a velocity of 34% speed of light and laser spectroscopic methods are used to measure the time dilation and compare it with theory of Special Relativity (SR).

June 28, 2008, at 01:31 AM by 92.75.9.198 -
Changed line 9 from:
to:

There are many open questions in the description of nature like how to combine gravity and quantum mechanics or what is dark matter/dark energy. Also CPT-symmetry and Lorentz-Transformation are under investigation if they are correct. In the following an experiment at GSI is presented as a continuation of a former experiment at MPI for nuclear physics which delivers one of the best test of Lorentz violation.

June 28, 2008, at 01:17 AM by 92.75.9.198 -
Changed lines 45-46 from:

At GSI the lithium ions ^7Li^+ are produced in an ECR ion source and is mainly accelerated by a linear accelerator (UNILAC) and a synchrotron (SIS). The final velocity is 0.338c or a kinetic energy of 409 MeV.

to:

At GSI the lithium ions ^7Li^+ are produced in an ECR ion source and is mainly accelerated by a linear accelerator (UNILAC) and a synchrotron (SIS). The final velocity is 0.338c or a kinetic energy of 409 MeV. The ions are stored in the experimental storage ring ESR and prepared for the laser spectroscopy.

June 28, 2008, at 01:14 AM by 92.75.9.198 -
Changed lines 45-46 from:

At GSI the lithium ions ^7Li^+ are produced in an ECR ion source and is mainly accelerated by a linear accelerator and a synchrotron. The final velocity is 0.338c or a kinetic energy of

to:

At GSI the lithium ions ^7Li^+ are produced in an ECR ion source and is mainly accelerated by a linear accelerator (UNILAC) and a synchrotron (SIS). The final velocity is 0.338c or a kinetic energy of 409 MeV.

June 28, 2008, at 01:13 AM by 92.75.9.198 -
Changed lines 45-46 from:
to:

At GSI the lithium ions ^7Li^+ are produced in an ECR ion source and is mainly accelerated by a linear accelerator and a synchrotron. The final velocity is 0.338c or a kinetic energy of

June 27, 2008, at 05:45 PM by 130.183.91.199 -
Changed lines 33-34 from:
\frac{\nu_0^2}{\nu_p\nu_a}=1+2\alpha\beta^2
.
to:
\frac{\nu_p\nu_a}{\nu_0^2}=1+2\alpha\beta^2
.
Changed lines 36-37 from:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent speed of light were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm. The results are published in (SaschaReinhardtNaturePhysics2007).

to:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent speed of light were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm. The results are published in (SaschaReinhardtNaturePhysics2007):

\alpha=(-4.8\pm 8.4)\cdot 10^{-8}

and for the transition frequency \nu_0 (if Special Relativity is ok)

\nu_0=546\ 466\ 918\ 531\pm 73) kHz
.
June 27, 2008, at 05:43 PM by 130.183.91.199 -
Changed lines 33-34 from:

{$$\frac{\nu_0^2}{\nu_p\nu_a}=1+2\alpha\beta^2$$].

to:
\frac{\nu_0^2}{\nu_p\nu_a}=1+2\alpha\beta^2
.
June 27, 2008, at 05:42 PM by 130.183.91.199 -
Changed lines 29-30 from:

To verify the last equatation only frequencies must be measured and no velocities must be known. Frequencies can be measured to a high accuarcy.

to:

To verify the last equation only frequencies must be measured and no velocities must be known. Frequencies can be measured to a high accuarcy.

For comparision of different experiments and the last relation can be written as (s. Testtheories)

{$$\frac{\nu_0^2}{\nu_p\nu_a}=1+2\alpha\beta^2$$].

June 27, 2008, at 05:32 PM by 130.183.91.199 -
June 27, 2008, at 05:31 PM by 130.183.91.199 -
Changed lines 32-33 from:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent speed of light were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm. The results are published in Invalid BibTex Entry!.

to:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent speed of light were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm. The results are published in (SaschaReinhardtNaturePhysics2007).

June 27, 2008, at 05:21 PM by 130.183.91.199 -
Changed lines 32-33 from:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm.

to:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent speed of light were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm. The results are published in Invalid BibTex Entry!.

June 27, 2008, at 03:44 PM by 130.183.91.199 -
Changed lines 13-14 from:
\nu_0=\nu_l*\gamma(1-\beta*cos(\theta)).
to:
\nu_0=\nu_l\gamma(1-\beta\cos(\theta)).
Changed lines 21-24 from:
\nu_0=\nu_p*\gamma(1-\beta)
\nu_0=\nu_a*\gamma(1+\beta)
\Rightarrow \nu_0^2=\nu_p*\nu_a*\gamma^2(1-\beta^2)
to:
\nu_0=\nu_p\gamma(1-\beta)
\nu_0=\nu_a\gamma(1+\beta)
\Rightarrow \nu_0^2=\nu_p\nu_a\gamma^2(1-\beta^2)
Changed lines 27-28 from:
\nu_0^2=\nu_p*\nu_a.
to:
\nu_0^2=\nu_p\nu_a.
June 27, 2008, at 03:43 PM by 130.183.91.199 -
Changed lines 17-18 from:
\gamma_{SR}=1/(1-\beta^2)^{1/2}.
to:
\gamma_{SR}=1/\sqrt{1-\beta^2}.
June 27, 2008, at 03:43 PM by 130.183.91.199 -
Changed lines 11-12 from:

The basic effect of the experiment is the Doppler effect as it is given in Special Relativity. The relation between the frequency $\nu_0$ in the rest of the moving ion and laser frequency $\nu_l$ in the lab frame is

to:

The basic effect of the experiment is the Doppler effect as it is given in Special Relativity. The relation between the frequency \nu_0 in the rest of the moving ion and laser frequency \nu_l in the lab frame is

Changed lines 15-28 from:

$\theta$ is the angle between the laser and ion direction. $\beta$ is the velocity in units of speed of light and $\gamma$ is the time dilation factor. In Special Relativity the time dilation factor is given by

$$\gamma_{SR}=1/(1-\beta^2)^{1/2}.$$

For $\theta=0$ or $\theta=\pi$ the cosine is $\pm 1$. The case $\theta=0$ is called parallel (signed with p) and $\theta=\pi$ (signed with a) is called antiparallel. Mulitpling these two cases you obtain

$$\nu_0=\nu_p*\gamma(1-\beta)$$ $$\nu_0=\nu_a*\gamma(1+\beta)$$ $$\Rightarrow \nu_0^2=\nu_p*\nu_a*\gamma^2(1-\beta^2)$$

If $\gamma=\gamma_{SR}$ it reduces to

$$\nu_0^2=\nu_p*\nu_a.$$

to:

\theta is the angle between the laser and ion direction. \beta is the velocity in units of speed of light and \gamma is the time dilation factor. In Special Relativity the time dilation factor is given by

\gamma_{SR}=1/(1-\beta^2)^{1/2}.

For \theta=0 or \theta=\pi the cosine is \pm 1. The case \theta=0 is called parallel (signed with p) and \theta=\pi (signed with a) is called antiparallel. Mulitpling these two cases you obtain

\nu_0=\nu_p*\gamma(1-\beta)
\nu_0=\nu_a*\gamma(1+\beta)
\Rightarrow \nu_0^2=\nu_p*\nu_a*\gamma^2(1-\beta^2)

If \gamma=\gamma_{SR} it reduces to

\nu_0^2=\nu_p*\nu_a.
June 27, 2008, at 03:41 PM by 130.183.91.199 -
Changed lines 13-14 from:

$$\nu_0=\nu_l*\gamma(1-\beta*cos(\theta)).$$

to:
\nu_0=\nu_l*\gamma(1-\beta*cos(\theta)).
June 27, 2008, at 02:10 PM by 130.183.91.199 -
June 27, 2008, at 11:52 AM by 130.183.91.199 -
Changed lines 13-14 from:
\nu_0=\nu_l*\gamma(1-\beta*\cos(\theta)).
to:

$$\nu_0=\nu_l*\gamma(1-\beta*cos(\theta)).$$

June 27, 2008, at 11:49 AM by 130.183.91.199 -
Changed lines 13-14 from:

$$\nu_0=\nu_l*\gamma(1-\beta*\cos(\theta)).$$

to:
\nu_0=\nu_l*\gamma(1-\beta*\cos(\theta)).
June 26, 2008, at 11:20 PM by 92.74.122.35 -
Changed lines 25-26 from:

If $\gamma=\gamma_{SR}$ is reduces to

to:

If $\gamma=\gamma_{SR}$ it reduces to

Changed lines 32-33 from:
to:

At the storage ring TSR in Heidelberg laser spectroscopy with ions at 3 percent and 6.4 percent were carried out. As transition a closed two level system of the metastable triplet and saturation spectroscopy was used. The transition wavelength is 548 nm. At 3% the parallel laser was a solid state laser at 532 nm and as parallel laser a dye laser at 565 nm was used. The laser for 6.4% were a dye laser at 585 nm and an argon ion laser 514 nm.

June 26, 2008, at 11:08 PM by 92.74.122.35 -
Changed lines 17-18 from:

$$\gamma_{SR}=1/\sqrt{1-\beta^2}.$$

to:

$$\gamma_{SR}=1/(1-\beta^2)^{1/2}.$$

June 26, 2008, at 11:07 PM by 92.74.122.35 -
Changed lines 17-28 from:

$$\gamma_{SR}=1/\sqrt(1-\beta^2).$$

For theta=0 or theta=pi the cosine is +/-1. The case theta=0 is called parallel (signed with p) and theta=pi (signed with a) is called antiparallel. Mulitpling these two cases you obtain

nu_0=nu_p*gamma(1-beta) nu_0=nu_a*gamma(1+beta) =>nu_0^2=nu_p*nu_a*gamma^2(1-beta^2)

If gamma=gamma_SR is reduces to

nu_0^2=nu_p*nu_a.

to:

$$\gamma_{SR}=1/\sqrt{1-\beta^2}.$$

For $\theta=0$ or $\theta=\pi$ the cosine is $\pm 1$. The case $\theta=0$ is called parallel (signed with p) and $\theta=\pi$ (signed with a) is called antiparallel. Mulitpling these two cases you obtain

$$\nu_0=\nu_p*\gamma(1-\beta)$$ $$\nu_0=\nu_a*\gamma(1+\beta)$$ $$\Rightarrow \nu_0^2=\nu_p*\nu_a*\gamma^2(1-\beta^2)$$

If $\gamma=\gamma_{SR}$ is reduces to

$$\nu_0^2=\nu_p*\nu_a.$$

June 26, 2008, at 11:04 PM by 92.74.122.35 -
Changed lines 11-18 from:

The basic effect of the experiment is the Doppler effect as it is given in Special Relativity. The relation between the frequency nu_0 in the rest of the moving ion and laser frequency nu_l in the lab frame is

nu_0=nu_l*gamma(1-beta*cos(theta)).

theta is the angle between the laser and ion direction. beta is the velocity in units of speed of light and gamma is the time dilation factor. In Special Relativity the time dilation factor is given by

gamma_SR=1/sqrt(1-beta^2).

to:

The basic effect of the experiment is the Doppler effect as it is given in Special Relativity. The relation between the frequency $\nu_0$ in the rest of the moving ion and laser frequency $\nu_l$ in the lab frame is

$$\nu_0=\nu_l*\gamma(1-\beta*\cos(\theta)).$$

$\theta$ is the angle between the laser and ion direction. $\beta$ is the velocity in units of speed of light and $\gamma$ is the time dilation factor. In Special Relativity the time dilation factor is given by

$$\gamma_{SR}=1/\sqrt(1-\beta^2).$$

June 26, 2008, at 10:29 PM by 92.74.122.35 -
Changed lines 13-14 from:
\nu_0=\nu_l*\gamma(1-\beta*\cos(\theta)).
to:

nu_0=nu_l*gamma(1-beta*cos(theta)).

June 26, 2008, at 10:28 PM by 92.74.122.35 -
June 26, 2008, at 10:26 PM by 92.74.122.35 -
Changed lines 13-14 from:

nu_0=nu_l*gamma(1-beta*cos(theta)).

to:
\nu_0=\nu_l*\gamma(1-\beta*\cos(\theta)).
June 26, 2008, at 12:21 AM by 92.75.24.222 -
Changed lines 27-28 from:

nu_0^2=nu_p*nu_a

to:

nu_0^2=nu_p*nu_a.

To verify the last equatation only frequencies must be measured and no velocities must be known. Frequencies can be measured to a high accuarcy.

June 26, 2008, at 12:18 AM by 92.75.24.222 -
Changed lines 11-28 from:
to:

The basic effect of the experiment is the Doppler effect as it is given in Special Relativity. The relation between the frequency nu_0 in the rest of the moving ion and laser frequency nu_l in the lab frame is

nu_0=nu_l*gamma(1-beta*cos(theta)).

theta is the angle between the laser and ion direction. beta is the velocity in units of speed of light and gamma is the time dilation factor. In Special Relativity the time dilation factor is given by

gamma_SR=1/sqrt(1-beta^2).

For theta=0 or theta=pi the cosine is +/-1. The case theta=0 is called parallel (signed with p) and theta=pi (signed with a) is called antiparallel. Mulitpling these two cases you obtain

nu_0=nu_p*gamma(1-beta) nu_0=nu_a*gamma(1+beta) =>nu_0^2=nu_p*nu_a*gamma^2(1-beta^2)

If gamma=gamma_SR is reduces to

nu_0^2=nu_p*nu_a

June 24, 2008, at 01:10 PM by 130.183.91.199 -
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### Illustration how the ions are accelerated to 0.34c at GSI

(:html:) <object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="320" height="270" id="player" align="middle"> <param name="movie" value="http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/player.swf?file=http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/gsi_ani.flv&size=false&aplay=false&autorew=false&title="/> <param name="menu" value="false"/> <param name="quality" value="high"/> <param name="bgcolor" value="#FFFFFF"/> <noscript><a href=http://www.dvdvideosoft.com/guides/avs/burn-video-files-to-DVD.htm>burn dvd</a></noscript> <embed src="http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/player.swf?file=http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/gsi_ani.flv&size=false&aplay=false&autorew=false&title=" menu="false" quality="high" bgcolor="#FFFFFF" width="320" height="270" name="player" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer"/> (:htmlend:)

### Laser spectroscopy at ESR

Deleted lines 122-137:

### Illustration how the ions are accelerated to 0.34c at GSI

(:html:) <object classid="clsid:d27cdb6e-ae6d-11cf-96b8-444553540000" codebase="http://fpdownload.macromedia.com/pub/shockwave/cabs/flash/swflash.cab#version=7,0,0,0" width="320" height="270" id="player" align="middle"> <param name="movie" value="http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/player.swf?file=http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/gsi_ani.flv&size=false&aplay=false&autorew=false&title="/> <param name="menu" value="false"/> <param name="quality" value="high"/> <param name="bgcolor" value="#FFFFFF"/> <noscript><a href=http://www.dvdvideosoft.com/guides/avs/burn-video-files-to-DVD.htm>burn dvd</a></noscript> <embed src="http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/player.swf?file=http://www.sascha-reinhardt.de/pmwiki/uploads/Physics/gsi_ani.flv&size=false&aplay=false&autorew=false&title=" menu="false" quality="high" bgcolor="#FFFFFF" width="320" height="270" name="player" align="middle" allowScriptAccess="sameDomain" type="application/x-shockwave-flash" pluginspage="http://www.macromedia.com/go/getflashplayer"/> (:htmlend:)

June 20, 2008, at 01:06 PM by 130.183.91.199 -
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};

to:

}

Changed line 57 from:

};

to:

}

June 20, 2008, at 12:55 PM by 130.183.91.199 -
Added line 46:

var dnu0=document.Enhancement.dnu0.value;

June 20, 2008, at 12:54 PM by 130.183.91.199 -
Added line 18:
• nu0=rest frequency transition of saturation two level system
Changed line 23 from:
• epsilon=nua*nup/(nu1*nu2)
to:
• epsilon=nua*nup/(nu1*nu2) (lambda) or epsilon=nua*nup/(nu0^2) (saturation)
June 20, 2008, at 12:53 PM by 130.183.91.199 -
Changed line 84 from:

Rest frequency transition saturation nu0 =(<input type="text" size="15" name="nu0" value="546466918.79">+/-<input type="text" size="15" name="dnu2" value="0.4">) MHz

to:

Rest frequency transition saturation nu0 =(<input type="text" size="15" name="nu0" value="546466918.79">+/-<input type="text" size="15" name="dnu0" value="0.4">) MHz

June 20, 2008, at 12:52 PM by 130.183.91.199 -
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var nu0=document.Enhancement.nu0.value;

Added lines 49-51:

if (document.Enhancement.Saturation.checked == true){ nu1nu2=nu0*nu0; };

Added lines 53-55:

if (document.Enhancement.Saturation.checked == true){ depsilon=Math.sqrt(Math.pow(dnua*nup/(nu0*nu0),2)+Math.pow(dnup*nua/(nu0*nu0),2)+Math.pow(2*nua*nup/(nu0*nu0*nu0)*dnu0,2)); };

June 20, 2008, at 12:48 PM by 130.183.91.199 -
Changed line 73 from:

Rest frequency transition 1=(<input type="text" size="15" name="nu1" value="546455144.8">+/-<input type="text" size="15" name="dnu1" value="0.4">) MHz

to:

Rest frequency transition lambda nu1=(<input type="text" size="15" name="nu1" value="546455144.8">+/-<input type="text" size="15" name="dnu1" value="0.4">) MHz

Changed line 75 from:

Rest frequency transition 2=(<input type="text" size="15" name="nu2" value="546474962.7">+/-<input type="text" size="15" name="dnu2" value="0.4">) MHz

to:

Rest frequency transition lambda nu2=(<input type="text" size="15" name="nu2" value="546474962.7">+/-<input type="text" size="15" name="dnu2" value="0.4">) MHz

Added lines 77-78:

Rest frequency transition saturation nu0 =(<input type="text" size="15" name="nu0" value="546466918.79">+/-<input type="text" size="15" name="dnu2" value="0.4">) MHz <br>

June 20, 2008, at 11:00 AM by 130.183.91.199 -
Added lines 29-34:

function uncheckl(){ document.Enhancement.Lambda.checked = false; } function unchecks(){ document.Enhancement.Saturation.checked = false; }

Changed line 80 from:

<input type="button" value="Calculate" onclick="EnhancementCal()">Saturation<input type="radio" name="Saturation" value="s" onclick="EnhancementCal()">Lambda<input type="radio" name="Lambda" value="l" onclick="EnhancementCal()" checked>

to:

<input type="button" value="Calculate" onclick="EnhancementCal()">Saturation<input type="radio" name="Saturation" value="s" onclick="uncheckl()">Lambda<input type="radio" name="Lambda" value="l" onclick="unchecks()" checked>

June 20, 2008, at 10:31 AM by 130.183.91.199 -
Changed line 74 from:

<input type="button" value="Calculate" onclick="EnhancementCal()">

to:

<input type="button" value="Calculate" onclick="EnhancementCal()">Saturation<input type="radio" name="Saturation" value="s" onclick="EnhancementCal()">Lambda<input type="radio" name="Lambda" value="l" onclick="EnhancementCal()" checked>

June 19, 2008, at 01:57 PM by 130.183.91.199 -
Added lines 3-4:

Table of contents

June 19, 2008, at 01:55 PM by 130.183.91.199 -
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to:

(:toc:)

June 19, 2008, at 01:55 PM by 130.183.91.199 -
Changed line 4 from:
to:

(:num:)

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(:htmlend:)

to:

(:htmlend:)

(:nonum:)

June 19, 2008, at 01:44 PM by 130.183.91.199 -
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"measured values"

to:

measured values

Changed lines 17-18 from:

"test parameters"

to:

test parameters

Changed line 21 from:
• alpha2=1/2*((epsilon-1-2*alphal*beta^2)/beta^4-alphal)
to:
• alpha2=1/2*((epsilon-1-2*alphal*beta^2)/beta^4-alphal) \\
June 19, 2008, at 01:43 PM by 130.183.91.199 -
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to:

### Determination of alpha and alpha2 parameters from Robertson-Mansouir-Sexl (RMS) test theory

In RMS several test parameters are introduced by expanding a function in velocity. For the experiment the relation between the test parameters and the measured values are:

"measured values"

• nua=frequency light antiparallel to ion movement
• nup=frequency light parallel to ion movement
• nu1=rest frequency transition 1 of lambda system
• nu2=rest frequency transition 2 of lambda system
• beta=velocity of ions

"test parameters"

• epsilon=nua*nup/(nu1*nu2)
• alpha=(epsilon-1)/(2*beta^2)
• alpha2=1/2*((epsilon-1-2*alphal*beta^2)/beta^4-alphal)

(alphal is a value for alpha obtained by another low velocity experiment)

June 19, 2008, at 01:33 PM by 130.183.91.199 -
June 19, 2008, at 01:26 PM by 130.183.91.199 -
Changed line 32 from:

dalpha2=1/2*Math.sqrt(Math.pow(depsilon/(beta*beta*beta*beta),2)+Math.pow((2/(beta*beta)+1)*dalphal));

to:

dalpha2=1/2*Math.sqrt(Math.pow(depsilon/(beta*beta*beta*beta),2)+Math.pow((2/(beta*beta)+1)*dalphal,2));

June 19, 2008, at 01:21 PM by 130.183.91.199 -
Changed lines 58-60 from:

epsilon=<input type="text" size="15" name="eps" value="1">+/-<input type="text" size="15" name="deps" value="0"> alpha=<input type="text" size="15" name="alpha" value="0">+/-<input type="text" size="15" name="dalpha" value="0"> alpha2(alphal)=<input type="text" size="15" name="alpha2" value="0">+/-<input type="text" size="15" name="dalpha2" value="0">

to:

epsilon=<input type="text" size="20" name="eps" value="1">+/-<input type="text" size="20" name="deps" value="0"> alpha=<input type="text" size="20" name="alpha" value="0">+/-<input type="text" size="20" name="dalpha" value="0"> alpha2(alphal)=<input type="text" size="20" name="alpha2" value="0">+/-<input type="text" size="20" name="dalpha2" value="0">

June 19, 2008, at 01:20 PM by 130.183.91.199 -
Added lines 20-21:

var alphal=document.Enhancement.alphal.value; var dalphal=document.Enhancement.dalphal.value;

Added lines 31-34:

alpha2=1/2*((epsilon-1-2*alphal*beta*beta)/(beta*beta*beta*beta)-alphal); dalpha2=1/2*Math.sqrt(Math.pow(depsilon/(beta*beta*beta*beta),2)+Math.pow((2/(beta*beta)+1)*dalphal)); document.Enhancement.alpha2.value=alpha2; document.Enhancement.dalpha2.value=dalpha2;

Changed line 59 from:

alpha=<input type="text" size="15" name="alpha" maxlength=4 value="0">+/-<input type="text" size="15" name="dalpha" value="0">

to:

alpha=<input type="text" size="15" name="alpha" value="0">+/-<input type="text" size="15" name="dalpha" value="0">

June 19, 2008, at 01:16 PM by 130.183.91.199 -
Changed line 53 from:

alpha=<input type="text" size="15" name="alpha" value="0">+/-<input type="text" size="15" name="dalpha" value="0">

to:

alpha=<input type="text" size="15" name="alpha" maxlength=4 value="0">+/-<input type="text" size="15" name="dalpha" value="0">

June 19, 2008, at 01:14 PM by 130.183.91.199 -
Added lines 25-28:

alpha=(epsilon-1)/(2*beta*beta); document.Enhancement.alpha.value=alpha; dalpha=(depsilon)/(2*beta*beta); document.Enhancement.dalpha.value=dalpha;

June 19, 2008, at 01:13 PM by 130.183.91.199 -
Changed line 24 from:

document.Enhancement.eps.value=depsilon;

to:

document.Enhancement.eps.value=epsilon;

June 19, 2008, at 01:12 PM by 130.183.91.199 -
Changed lines 21-22 from:

var epsilon=Math.sqrt(Math.pow(dnua*nup/(nu1nu2),2)+Math.pow(dnup*nua/nu1nu2,2)+Math.pow(nua*nup*dnu1/(nu1*nu1nu2),2)+Math.pow(nua*nup*dnu2/(nu2*nu1nu2),2)); document.Enhancement.eps.value=epsilon;

to:

var depsilon=Math.sqrt(Math.pow(dnua*nup/(nu1nu2),2)+Math.pow(dnup*nua/nu1nu2,2)+Math.pow(nua*nup*dnu1/(nu1*nu1nu2),2)+Math.pow(nua*nup*dnu2/(nu2*nu1nu2),2)); document.Enhancement.deps.value=depsilon; epsilon=nua*nup/nu1nu2; document.Enhancement.eps.value=depsilon;

June 19, 2008, at 01:10 PM by 130.183.91.199 -
Changed line 21 from:

var epsilon=Math.sqrt(Math.pow(dnua*nup/(nu1nu2))+Math.pow(dnup*nua/nu1nu2)+Math.pow(nua*nup*dnu1/(nu1*nu1nu2))+Math.pow(nua*nup*dnu2/(nu2*nu1nu2)));

to:

var epsilon=Math.sqrt(Math.pow(dnua*nup/(nu1nu2),2)+Math.pow(dnup*nua/nu1nu2,2)+Math.pow(nua*nup*dnu1/(nu1*nu1nu2),2)+Math.pow(nua*nup*dnu2/(nu2*nu1nu2),2));

June 19, 2008, at 01:09 PM by 130.183.91.199 -
Changed lines 11-16 from:

var IC=document.Enhancement.IC.value; var AIC=document.Enhancement.AIC.value; var R=document.Enhancement.R.value; var N=document.Enhancement.N.value; var T=document.Enhancement.T.value; document.Enhancement.U.value=(1-IC-AIC)/Math.pow(1-Math.sqrt(IC*T*Math.pow(R,N)),2);

to:

var nua=document.Enhancement.nua.value; var nup=document.Enhancement.nup.value; var nu1=document.Enhancement.nu1.value; var nu2=document.Enhancement.nu2.value; var dnua=document.Enhancement.dnua.value; var dnup=document.Enhancement.dnup.value; var dnu1=document.Enhancement.dnu1.value; var dnu2=document.Enhancement.dnu2.value; var beta=document.Enhancement.beta.value; var nu1nu2=nu1*nu2; var epsilon=Math.sqrt(Math.pow(dnua*nup/(nu1nu2))+Math.pow(dnup*nua/nu1nu2)+Math.pow(nua*nup*dnu1/(nu1*nu1nu2))+Math.pow(nua*nup*dnu2/(nu2*nu1nu2))); document.Enhancement.eps.value=epsilon;

Deleted lines 23-31:

function FinesseCal (){ var IC=document.Enhancement.IC.value; var AIC=document.Enhancement.AIC.value; var R=document.Enhancement.R.value; var N=document.Enhancement.N.value; var T=document.Enhancement.T.value; document.Finesse.F.value=Math.PI*Math.sqrt(Math.sqrt(Math.pow(R,N)*IC*T))/(1-Math.sqrt(Math.pow(R,N)*IC*T)); }

June 19, 2008, at 01:05 PM by 130.183.91.199 -
Added lines 33-34:

ion velocity in units of speed of light beta=<input type="text" size="15" name="beta" value="0.338"> <br>

Changed line 43 from:

alpha obtained from low velocity=(<input type="text" size="15" name="alphal" value="0">+/-<input type="text" size="15" name="dalphal" value="8.4e-8">)

to:

alpha obtained from low velocity alphal=(<input type="text" size="15" name="alphal" value="0">+/-<input type="text" size="15" name="dalphal" value="8.4e-8">)

Changed lines 45-47 from:

Reflectivity other mirrors R <input type="text" size="40" name="R" value="0.98"> Number of reflections other mirrors N <input type="text" size="40" name="N" value="5"> Transparency medium T <input type="text" size="40" name="T" value="1">

to:

<div align="center">

Changed lines 47-48 from:

Enhancement <input type="text" size="40" name="U" value="0">

to:

</div> <div align="right"> epsilon=<input type="text" size="15" name="eps" value="1">+/-<input type="text" size="15" name="deps" value="0"> alpha=<input type="text" size="15" name="alpha" value="0">+/-<input type="text" size="15" name="dalpha" value="0"> alpha2(alphal)=<input type="text" size="15" name="alpha2" value="0">+/-<input type="text" size="15" name="dalpha2" value="0"> </div>

June 19, 2008, at 12:59 PM by 130.183.91.199 -
Changed line 41 from:

alpha obtained from low velocity=(<input type="text" size="15" name="alphal" value="0">+/-<input type="text" size="15" name="dalphal" value="8.4e-8">)

to:

alpha obtained from low velocity=(<input type="text" size="15" name="alphal" value="0">+/-<input type="text" size="15" name="dalphal" value="8.4e-8">)

June 19, 2008, at 12:58 PM by 130.183.91.199 -
Added lines 40-41:

<br> alpha obtained from low velocity=(<input type="text" size="15" name="alphal" value="0">+/-<input type="text" size="15" name="dalphal" value="8.4e-8">)

June 19, 2008, at 12:56 PM by 130.183.91.199 -
Added lines 36-39:

<br> Rest frequency transition 1=(<input type="text" size="15" name="nu1" value="546455144.8">+/-<input type="text" size="15" name="dnu1" value="0.4">) MHz <br> Rest frequency transition 2=(<input type="text" size="15" name="nu2" value="546474962.7">+/-<input type="text" size="15" name="dnu2" value="0.4">) MHz

June 19, 2008, at 11:28 AM by 130.183.91.199 -
Added lines 34-35:

<br> Frequency antiparallel laser beam nua=(<input type="text" size="15" name="nua" value="384228270">+/-<input type="text" size="15" name="dnua" value="86">) MHz

Deleted lines 36-38:

<div align="right"> Frequency antiparallel laser beam nua=(<input type="text" size="15" name="nua" value="384228270">+/-<input type="text" size="15" name="dnua" value="86">) MHz </div>

June 19, 2008, at 11:27 AM by 130.183.91.199 -
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<div align="right">

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</div> <div align="right">

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</div>

June 19, 2008, at 11:23 AM by 130.183.91.199 -
Changed lines 32-33 from:

Frequency parallel laser beam nup=(<input type="text" size="40" name="nup" value="777204676">+/-<input type="text" size="40" name="dnup" value="200">) MHz Frequency antiparallel laser beam nua=(<input type="text" size="40" name="nua" value="384228270">+/-<input type="text" size="40" name="dnua" value="86">) MHz

to:

Frequency parallel laser beam nup=(<input type="text" size="15" name="nup" value="777204676">+/-<input type="text" size="15" name="dnup" value="200">) MHz Frequency antiparallel laser beam nua=(<input type="text" size="15" name="nua" value="384228270">+/-<input type="text" size="15" name="dnua" value="86">) MHz

June 19, 2008, at 11:23 AM by 130.183.91.199 -
Changed lines 32-33 from:

Reflectivity input coupler IC <input type="text" size="40" name="IC" value="0.92"> Absorption input coupler AIC <input type="text" size="40" name="AIC" value="0.005">

to:

Frequency parallel laser beam nup=(<input type="text" size="40" name="nup" value="777204676">+/-<input type="text" size="40" name="dnup" value="200">) MHz Frequency antiparallel laser beam nua=(<input type="text" size="40" name="nua" value="384228270">+/-<input type="text" size="40" name="dnua" value="86">) MHz

June 19, 2008, at 11:07 AM by 130.183.91.199 -
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to:

### Illustration how the ions are accelerated to 0.34c at GSI

June 19, 2008, at 11:07 AM by 130.183.91.199 -
Changed lines 3-4 from:
to:

### Determination of alpha and alpha2 parameters from Robertson-Mansouir-Sexl test theory

(:html:) <script language="JavaScript"> <!-- function EnhancementCal (){ var IC=document.Enhancement.IC.value; var AIC=document.Enhancement.AIC.value; var R=document.Enhancement.R.value; var N=document.Enhancement.N.value; var T=document.Enhancement.T.value; document.Enhancement.U.value=(1-IC-AIC)/Math.pow(1-Math.sqrt(IC*T*Math.pow(R,N)),2); }

function FinesseCal (){ var IC=document.Enhancement.IC.value; var AIC=document.Enhancement.AIC.value; var R=document.Enhancement.R.value; var N=document.Enhancement.N.value; var T=document.Enhancement.T.value; document.Finesse.F.value=Math.PI*Math.sqrt(Math.sqrt(Math.pow(R,N)*IC*T))/(1-Math.sqrt(Math.pow(R,N)*IC*T)); } //--> //--> </script> <form name="Enhancement"> <pre> Reflectivity input coupler IC <input type="text" size="40" name="IC" value="0.92"> Absorption input coupler AIC <input type="text" size="40" name="AIC" value="0.005"> Reflectivity other mirrors R <input type="text" size="40" name="R" value="0.98"> Number of reflections other mirrors N <input type="text" size="40" name="N" value="5"> Transparency medium T <input type="text" size="40" name="T" value="1"> <input type="button" value="Calculate" onclick="EnhancementCal()"> Enhancement <input type="text" size="40" name="U" value="0">

</pre> </form> (:htmlend:)

June 05, 2008, at 01:13 PM by 130.183.91.199 -
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(:html:)

to:

(:html:)

June 05, 2008, at 01:12 PM by 130.183.91.199 -
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## Time dilation experiment at 34%c using laser spectroscopy

June 05, 2008, at 01:08 PM by 130.183.91.199 -
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