Abstract:
A volume calibration phantom comprises a container; a plurality of plates stacking up inside the container; and at least one slab of radioactive source, each of which is disposed between the adjacent plates and comprises a plurality of radionuclides. With the volume calibration phantoms, the present invention further provides a calibration method which is an improvement over conventional calibration methods of space geometric center point source and relative penetration factor ratios. The method comprises the steps of generating a calibration curve of density vs. counting efficiency corresponding to the several different volume calibration phantoms; calculating the density of a radioactive waste specimen to obtain a corresponding radioactive activity according to the calibration curve, and then revising the corresponding radioactive activity according to the energy dependency and equation of gamma gross radioactivity for multiple radionuclides so as to obtain the correct gamma gross radioactivity of the radioactive waste specimen.

Description:
FIELD OF THE INVENTION 
   The present invention relates to a volume calibration phantom and calibration method thereof, and more particularly, to a calibration method for calibrating phantoms of various densities, by which a corresponding calibration curve of density against counting efficiency can be obtained and used as reference for obtaining a sample gross gamma radioactivity of a test sample while calibrating the sample gamma gross radioactivity by a calibration formula for acquiring a correct gross gamma radioactivity. 
   BACKGROUND OF THE INVENTION 
   Currently, waste curie monitors, being substantially an assembly of several large-area plastic scintillation detectors, are frequently used at nuclear facilities and organizations for measuring the gross gamma radioactivity of very low radioactive wastes. The aforesaid monitors are advantageous in its high radioactive sensitivity, high counting efficiency, short counting interval required for counting a test sample, no restriction to the volume of the waste to be monitored thereby, and capability of revealing the weight of the waste monitored thereby, and so on. 
   However, the aforesaid monitors still have drawbacks list as following: (1) The radioactivity measured thereby is often overestimated or under-estimated, since it only accounts for the weight of a waste sample tested thereby and overlooks the deviations of various self-absorption effects caused by the various densities of different waste samples. (2) Since the calibration curve used in aforesaid monitors is based upon the measurement of an object made up of a pure substance that it overlooks the fact that any usual waste sample is made up of more than one substance, the so-established calibration curve is not appropriate. (3) For calibrating the aforesaid monitor, phantom is being positioned at the geometric center of the monitor, that is not relative to the positioning of a waste sample on the floor of the aforesaid monitor as it is being measured. (4) As there is no restriction regarding to the volume of a waste sample to be measured by the aforesaid monitor, the distances between the tested sample and the scintillation detectors are not conforming to those of a phantom as being used for building a calibration curve, and thus error in radioactivity measurement will occur so that the accuracy of radioactivity measurement required by Regulation of radiation protection can not be achieved. (5) The corresponding radioactive activity with respect to the energy dependency and equation of gamma gross radioactivity for multiple radionuclides are not revised, so that the gamma gross radioactivity of the radioactive a waste sample measured thereby is not accurate. 
   In recent years, an improvement over conventional calibration methods of space geometric center point source is being developed for performing gross gamma radioactivity measurement upon waste samples while using the measurement for classifying wastes into radioactive wastes and non-radioactive wastes. Currently, there are several calibration methods for plastic scintillation detectors, which are listed as following: (1) The calibration method developed by Themo-Eberline adopts a means of transmission factor (TF) for calibrating self-absorption effects of various standard mass, in that, the transmission factor is defined as the ratio of the dose inside the shielding material to the outside (ambient) dose, whereas TF≦1.0 refers to the calibration of non-shield radioactive source positioned in the geometric center of a space filled with air. Moreover, as TF is defined to be 1, the mass of a radioactive material containing in a water phantom can be determined whereas 10 kg is being defined as a unit, and thus, a calibration file corresponding thereto can be established Thereby, the gross gamma radioactivity of a waste sample can be calibrated with respect to the comparison between the weight of the tested waste sample and its standard mass of TF=1; (2) The method, developed by RADOS company, Germany, adopts a pure iron plate assembly for calibrating; (3) The method, developed by Japan Nuclear Energy Safety Organization, adopts an assembly of metal tubes and metal plates for multi-radionuclides calibration; (4) The method, developed by NE Technology company, USA, adopts multi-radionuclides point sources and a pure Brazil wood of density equal to one for performing a multi-weight calibration (0˜60 kg). However, those currently available calibration methods only account for general masses and geometrical shapes, they still can not deal with the self-absorption effects of a waste sample of various masses as well as their energy dependency, and thus the gross gamma radioactivity acquired thereby is not accurate. 
   Therefore, it is in need of a volume calibration phantom and calibration method thereof, which free from the problems of prior arts. 
   SUMMARY OF THE INVENTION 
   It is the primary object of the present invention to provide a calibration method for calibrating phantoms of various densities, by which a corresponding calibration curve of density against counting efficiency can be obtained and used as reference for obtaining a sample gross gamma radioactivity of a test sample while calibrating the sample gamma gross radioactivity by a calibration formula for acquiring a correct gross gamma radioactivity. 
   It is another object of the invention to provide a volume calibration phantom and calibration method thereof, which can be used for evaluating energy dependency so as to use the evaluation for calibrating the gross gamma radioactivity of various waste samples. 
   Yet, another object of the invention is to provide a volume calibration phantom and calibration method thereof, which use a standard container, whose volume and dimensions are the same as those of the volume calibration phantom, for enabling a waste sample to be tested and measured at a condition similar to that of the volume calibration phantom and thus acquiring an accurate radioactivity corresponding thereto. 
   To achieve the above objects, the present invention provides a volume calibration phantom, being disposed inside a monitor having a plurality of radiation detectors received inside a accommodation space formed inside the monitor, that the volume calibration phantom is comprised of: a container; a plurality of plates, stacking up inside the container; and at least one slab of radioactive source, each of which is disposed between the adjacent plates and comprises a plurality of radionuclides. 
   Preferably, each plate is made of a metal such as iron. 
   Preferably, each plate is made of a non-metal material where as the non-metal material is a material selected from the group consisting of paper, wood, gypsum, acrylic resin, rubber and glass. 
   Preferably, any one of the plural radionuclides is a gamma radioactive source, and can be a radionuclide selected from the group consisting of  57 Co,  54 Mn,  60 Co,  137 Cs and the combination thereof 
   Preferably, any one of the plural radionuclides is a radioactive source of circular shape, and the diameter of the circular-shaped radioactive source is smaller than 5 cm. 
   Preferably, each slab of radioactive source is comprised of: a bottom laminating layer; a leakage-prevention filter layer, formed on the bottom laminating layer while having the plural radionuclides to be formed thereon; and a top laminating layer, formed on top of the leakage-prevention filter layer as the protection of the plural radionuclides. 
   In a preferred aspect, present invention provides a calibration method, comprising steps of: providing a plurality of volume calibration phantoms of various densities; measuring the plural volume calibration phantoms by a specific monitor for obtaining a calibration curve of density against counting efficiency corresponding to the measurement; filling a waste specimen into a container of the same volume as each of the plural volume calibration phantoms so as to be used as a test sample; obtaining a sample gamma gross radioactivity of the test sample by referencing to the calibration curve with respect to the density of the test sample measured and detected by the specific monitor; and calibrating the sample gamma gross radioactivity by a calibration formula for acquiring a correct gamma gross radioactivity. 
   Preferably, the sample gamma gross radioactivity can be calibrated with respect to an energy dependency factor and a formula of multi-radionuclides calculation. 
   Other aspects and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the present invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic diagram showing a volume calibration phantom and a waste curie monitor. 
       FIG. 2A  is a schematic diagram showing a standard container of the invention. 
       FIG. 2B  shows the stacking of pates and slabs of radioactive sources according to the present invention. 
       FIG. 3A  is cross-sectional view of a slab of radioactive sources according to the present invention. 
       FIG. 3B  is a schematic diagram depicting the distribution of radionuclides on a slab of radioactive sources according to the present invention. 
       FIG. 4  shows the steps of a calibration method of the invention. 
       FIG. 5  shows the minimum detectable activities (MDAs) of radionuclides of different densities according to the present invention. 
       FIG. 6  shows the relationship between counting time and MDAs according to the present invention. 
       FIG. 7  shows the variations of photonic efficiency with respect to of calibration phantoms of different densities. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENT 
   For your esteemed members of reviewing committee to further understand and recognize the fulfilled functions and structural characteristics of the invention, several preferable embodiments cooperating with detailed description are presented as the follows. 
   Please refer to  FIG. 1 , which is a schematic diagram showing a volume calibration phantom and a waste curie monitor. The waste curie monitor  1  of  FIG. 1  is substantially a shield box  10  whose six walls is made of lead with equal thickness, in which an inspection space  100  is formed while having six large-area radiation detectors  11  being arranged respectively on the inner walls of the shield box  10  encasing the inspection space  100 . In this preferred embodiment of the invention, each large-area radiation detector  11  can be a plastic scintillation detector. Moreover, a weight meter is disposed in the inspection space  100  for weighting an object-to-be-tested. In addition, the waste curie monitor is connected to a computer  12 , which is programmed with a software and calibration parameters for performing operations such as counting the radioactivity (Bq) or specific radioactivity (Bq/g) in a sample and its back ground, calibrating the minimum detectable activity (MDA) of the monitor, and printing and displaying the result of a detection. 
   As seen in  FIG. 1 , a volume calibration phantom  2  of uniform radioactivity is received in the inspection space  100 . Please refer to  FIG. 2A  and  FIG. 2B , which are schematic diagrams respectively showing a standard container and the stacking of plates and slabs of radioactive sources according to the present invention. The volume calibration phantom  2  is substantially a stacking of uniform plates  22  and slabs of radioactive source  23 , being disposed in an inner space  21  of a standard container  20 . In a preferred aspect, each plate  21  can be made of a metallic material or a non-metallic material, whereas the metallic material can be iron; and the non-metallic material can be paper, wood, gypsum, acrylic resin, rubber or glass. 
   In a preferred embodiment of the invention, uniform plates made of seven different materials are being cut into plates of 33 cm wide, 33 cm long and 1 cm thick, and are stacked to form a calibration phantom about the same size as the standard container  20 , that is about 33 cm long, 33 cm wide and 30 cm height, while enabling the weight of the calibration phantom to be ranged between 5 kg to 100 kg. The average density of the calibration phantom can be acquired with respect to its volume, i.e. 33 cm 3 . In a preferred aspect, the calibration phantom is a multi-density calibration phantom, composing of paper plates at a density of 0.15 gcm −3 , wood plates at a density of 0.55 gcm −3 , gypsum plates at a density of 0.75 gcm −3 , acrylic plates at a density of 1.13 gcm −3 , rubber plates at a density of 1.80 gcm −3 , glass plate at a density of 2.5 gcm −3 , and iron plates at a density of 3 gcm −3 . 
   In the calibration phantom, there are seven large-area slabs of radioactive source being sandwiched respectively between adjacent plates. Please refer to  FIG. 3A , which is cross-sectional view of a slab of radioactive sources according to the present invention. As seen in  FIG. 3A , each of the large-area slabs of radioactive source  23  is comprised of: a bottom laminating layer  233 ; a leakage-prevention filter layer  232 , formed on the bottom laminating layer  233 , a radiation source layer  231  with a plurality of radionuclides, formed on the leakage-prevention filter layer  232 ; and a top laminating layer  230 , formed on top of the leakage-prevention filter layer  232 , wherein, by the cooperation of the top and bottom laminating layers  230 ,  233 , the plural radionuclides of the radiation source layer  231  are protected. 
   Preferably, any one of the plural radionuclides can be a gamma radioactive source, and can be a radionuclide selected from the group consisting of  57 Co,  54 Mn,  60 Co,  137 Cs and the combination thereof. Please refer to  FIG. 3B , which is a schematic diagram depicting the distribution of radionuclides on a slab of radioactive sources according to the present invention. In  FIG. 3B , a 6×6 matrix is formed on the radiation source layer  231  that a total of 36 drops of 0.2 cc liquid-state radioactive sources  2310  are dripped respectively onto each area of the 6×6 matrix while each drop of the liquid-state radioactive source  2310  is spread into a circle whose diameter is smaller than 5 cm, while the 36 circles are not overlapped with each other. It is noted that the gross radioactivity of large-area slabs of  57 Co,  54 Mn ,  60 Co,  137 Cs are respectively 58 kBg, 72 kBg, and 90 kBg. As there are four different energies and seven different densities, 28 calibration phantoms of different energy and different densities can be established. 
   Please refer to  FIG. 4 , which shows the steps of a calibration method of the invention. The steps of the calibration method are listed and classified into four categories as following: 
   (1) Density and Count Efficiency Calibration: 
   In this category, a plurality of multi-radionuclides phantoms of various densities are provided, which is referred as step  30 . Thereafter, the plural calibration phantoms are measured by a specific monitor for obtaining a calibration curve of density against counting efficiency correspondingly, referring as step  31 . 
   (2) Photonic Energy Dependency 
   In order to evaluate the ratio difference of various gamma energy with respect to that of  137 Cs, large-area gamma radioactive sources of  57 Co of 122 keV and 136 keV,  54 Mn of 834 keV,  60 Co of 1173 keV and 1332 keV,  137 Cs of 662 keV, are placed respectively at the geometrical center of a waste curie monitor for measuring, and thus the radionuclide counting efficiency of gamma nuclides  57 Co,  54 Mn,  60 Co,  137 Cs, obtained from the measurement, are divided respectively by the energy branching ratios corresponding thereto, which are  57 Co: 96%,  54 Mn: 100%,  60 Co: 200%,  137 Cs: 85%, by which a diagram regarding to the photonic efficiency and energy of radionuclides  57 Co,  54 Mn,  60 Co,  137 Cs of various densities can be charted as seen in  FIG. 7  that the photonic efficiency is increasing with the increase of the energy. At high energy level, the variation of density will have more influence upon the photonic efficiency, and at low energy, the influence is less. Moreover, the photonic efficiency ratio of  57 Co,  54 Mn,  60 Co with respect to  137 Cs is illustrated in Table 1 as following: 
                                                               TABLE 1                   photonic efficiency ratio of waste curie monitor                density (g/cm 3 )     57 Co/ 137 Cs     54 Mn/ 137 Cs     60 Co/ 137 Cs                            0.15   0.40   1.25   1.49           0.5   0.32   1.18   1.44           0.75   0.26   1.13   1.41           1.13   0.23   1.01   1.30           1.8   0.17   0.79   1.11           2.5   0.16   0.77   0.99           3.0   0.08   0.63   0.85                        
(3) Waste Sample Measurement
 
   In this category, a step  32  is first being performed, in which a waste specimen is filled into a container of the same volume as each of the plural volume calibration phantoms so as to be used as a test sample, and then the process proceeds to step  33 . At step  33 , the weight of the test sample is measured by the monitor for obtaining the density of the same, by which a sample gamma gross radioactivity of the test sample can be obtained by referencing to the calibration curve with respect to the density of the test sample, and then the process proceeds to step  34 . At step  34 , the sample gamma gross radioactivity is calibrated by an energy dependency factor and a formula of multi-radionuclides calculation for acquiring a correct gamma gross radioactivity. 
   (4) In order to match the limit of radionuclide radioactivity, it is required for a waste curie monitor to have a correct method for calculating gross gamma radioactivity. Moreover, when a waste sample is verified as a multi-radionuclide waste sample, primarily comprising  54 Mn ,  60 Co,  137 Cs, it is required that the deviation of correctness for the radioactivity analysis of each radionuclide to be maintained within a specific tolerance.
 
(4-1) Minimum Detectable Activity (MDA)
 
   The formula for calculating minimum detectable activity (MDA), defined by US Nuclear Regulatory Commission (USNRC), NUREG-1507(1998), is as following: 
   
     
       
         
           MDA 
           = 
           
             3 
             + 
             
               4.65 
               ⁢ 
               
                 
                   
                     C 
                     BG 
                   
                 
                 
                   ɛ 
                   × 
                   t 
                 
               
             
           
         
       
     
       
       
         
           wherein 3+4.65 is defined as the limit of detector with 95% reliability
           C BG  is defined as counts per second (cps)   ε is defined as radionuclide counting efficiency   t is defined as counting time (sec)   
         
           when the average background counting is 1500, the MDAs of  57 Co,  54 Mn,  60 Co,  137 Cs of various average densities, detected and measured by a Eberline WCM-10PC within two-minute interval, are illustrated in Table 2 and  FIG. 5 . It is noted that the MDAs of  60 Co and  137 Cs at every average density are coincidence, that is, when the average density is within the range between 1 gcm −3  and 2 gcm −3 , the MDAs of  60 Co and  137 Cs are at their minimum; and when the average density is smaller than 1 gcm −3  or larger than 2 gcm −3 , the MDAs of  60 Co and  137 Cs are respectively 0.003 Bq/g and 0.010 Bq/g, which are about twice the MDAs of  60 Co and  137 Cs when their average density is between 1 gcm −3  and 2 gcm −3 . As the variation of weight is linear and the variation of geometrical center efficiency of radionuclide is an index trend, when the weight is too light or too heavy, the variation of efficiency will be larger than that of weight. Therefore, the MDAs of  60 Co are smaller than those of  137 Cs when the two are at the same average density. 
         
       
     
  
   The largest MDAs of  54 Mn ,  60 Co,  137 Cs are respectively 0.006 Bq/g, 0.001 Bq/g and 0.010 Bq/g. As the energy of  54 Mn is similar to that of  137 Cs, the MDAs of the two are similar no matter they are contained in cloth, water, iron tube or steel bar. In addition, the aforesaid MDAs of  54 Mn,  60 Co,  137 Cs all match the release limit defined by authority, that is, they should be 10 times lower than the radionuclide release limit defined by IAEA, e.q.  54 Mn,  60 Co,  137 Cs are all defined to be 0.1 Bq/g. In addition, according to the operation manual of the waste curie monitor 3300-200 by Antech company, the MDAs of  60 Co and  137 Cs at two-minute interval are respectively 0.006 Bq/g and 0.015 Bq/g, which are similar to those detected by the monitor used in the present invention. Moreover, by observing the relationship of MDAs , detected by plastic scintillation detectors, and time, the result of the MDA variations of  60 Co and  137 Cs are shown in  FIG. 6  as the counting times are set to be 1 min, 2 min, 5 min, 8 min and 10 min. As the counting time is extended from 1 min to 5 min, the MDAs of  60 Co and  137 Cs are lowered respectively by 1.9 times and 2 times. As the counting time is extended from 1 min to 10 min, the MDAs of  60 Co and  137 Cs are lowered respectively by 205 times and 2.7 times. As the counting time is extended from 8 min to 10 min, the MDAs of  60 Co and  137 Cs are lowered respectively by 9% and 15%, which is not significant. 
                                                               TABLE 2                   MDA of waste curie minotor (Bq/g)            density                       (g/cm 3 )     57 Co     54 Mn     137 Cs     60 Co                    0.15   0.059   0.018   0.019   0.0095       0.5   0.021   0.0058   0.0061   0.0029       0.75   0.018   0.004   0.0042   0.002       1.13   0.013   0.003   0.0032   0.0014       1.8   0.0084   0.0017   0.0018   0.00075       2.5   0.0088   0.0018   0.0018   0.00083       3.0   0.015   0.0019   0.002   0.0008                    
(4-2) Calculation Formula
 Total count:  M=A   i ε i   p   i Σ(1 +R   x   E   x )         wherein A i  is the radioactivity of  137 Cs (Bq/g)
           ε i  is the photonic efficiency of  137 Cs at 662 keV   p i  is the energy branching ratios of  137 Cs at 662 keV   R x  is the specific activity of each radionuclides against  137 Cs   E x  is the detection efficiency of each radionuclides against  137 Cs
 
radioactivity ratio:  R   x   =A   x   /A   i   (a)
   
           wherein A x  is the radioactivity of a radionuclide (HPGe analysis)
 
ratio of detection efficiency:  E   x =Σε x   p   x /ε i   p   i   (b)
   wherein ε x  is a detection efficiency of a radionuclides (%)
           p x  is anenergy branching ratio of a radionuclide (%)
 
gross gamma radioactivity:  A   t   =M/E   i   (c)
   
           wherein the detection efficiency of  137 Cs is E i =ε i p i 
 
index radionuclide radioactivity:  A   i   =A   t /Σ(1 +R   x   E   x )  (d)
   any radionuclide radioactivity: A x =A i ×R x      (e) release limit:       
   
     
       
         
           
             
               ∑ 
               x 
             
             ⁢ 
             
               
                 A 
                 x 
               
               / 
               
                 A 
                 
                   x 
                   , 
                   0 
                 
               
             
           
           ≤ 
           1 
         
       
     
       
       
         
           
             
               wherein A x,0  is the radioactivity limit of a radionuclide
 
(4-3) Multi-nuclide Analysis
 
             
           
         
       
     
  
   The standard total radioactivity of the seven uniform radionuclides placed inside the calibration phantom, i.e.  137 Cs (72105 Bq),  54 Mn (45309 Bq),  60 Co (86045 Bq) and  57 Co (42777 Bq), is 246239 Bq. The radioactivity ratio  57 Co:  54 Mn:  60 Co:  137 Cs is 0.593: 0.628: 1.19: 1. Thus, the total gross radioactivity, using a sample of  137 Cs at 1.1 gcm −3 , 1.8 gcm −3 , and 2.5 gcm −3 , is shown in Table 3. After the radioactivity of the aforesaid four radionuclides are calibrated by the foregoing formulas, the deviations of correctness form the standard total radioactivity are respectively 1.82%, 2.59% and 1.74%. 
   (4-3-1)  137 Cs efficiency of 1.1 gcm −3  phantom 
   as the index nuclide radioactivity A i  is  137 Cs, the gross radioactivity A t =321197 Bq, and the E x  of  57 Co,  54 Mn,  60 Co with respect to  137 Cs are 0.23, 1.01, and 1.30. 
   Thus, 
                   A   i     =       A   t     /     ∑     (     1   +       R   x     ⁢     E   x         )                     =     321197   /     [     1   +     (     0.593   ×   0.23     )     +     (     0.628   ×   1.01     )     +     (     1.19   ×   1.30     )       ]                   =     73500   ⁢           ⁢   Bq                   A   x   =A   i   ×R   x , therefore,  57 Co= A   i ×0.593=43586 Bq   54 Mn= A   i ×0.628=46158 Bq   60 Co= A   i ×1.19=87465 Bq         Hence, the calibrated gross gamma radioactivity A t =250709 Bq   the standard gross gamma radioactivity is 246239 Bq   the deviation of correctness is 3.36%
 
(4-3-2)  137 Cs efficiency of 1.8 gcm −3  phantom
       
   as the index nuclide radioactivity A i  is  137 Cs, the gross radioactivity A t =327780 Bq, and the E x  of  57 Co,  54 Mn,  60 Co with respect to  137 Cs are 0.17, 1.79, and 1.11. 
   Thus 
                   A   i     =       A   t     /     ∑     (     1   +       R   x     ⁢     E   x         )                     =     327780   /     [     1   +     (     0.593   ×   0.17     )     +     (     0.628   ×   0.79     )     +     (     1.19   ×   1.11     )       ]                   =     74058   ⁢           ⁢   Bq                   A   x   =A   i   ×R   x , therefore,  57 Co= A   i ×0.593=43916 Bq   54 Mn= A   i ×0.628=46508 Bq   60 Co= A   i ×1.19=88129 Bq 
   Hence, the calibrated gross gamma radioactivity A t =252611 Bq
         the standard gross gamma radioactivity is 246239 Bq   the deviation of correctness is 2.59%
 
(4-3-3)  137 Cs efficiency of 2.5 gcm −3  phantom
       

   as the index nuclide radioactivity A i  is  137 Cs, the gross radioactivity A t =325651 Bq, and the E x  of  57 Co,  54 Mn,  60 Co with respect to  137 Cs are 0.16, 0.77, and 0.99. 
   Thus, 
                   A   i     =       A   t     /     ∑     (     1   +       R   x     ⁢     E   x         )                     =     325651   /     [     1   +     (     0.593   ×   0.16     )     +     (     0.628   ×   0.77     )     +     (     1.19   ×   0.99     )       ]                   =     185345   ⁢           ⁢   Bq                   A   x   =A   i   ×R   x , therefore,  57 Co= A   i ×0.593=43552 Bq   54 Mn= A   i ×0.628=46123 Bq   60 Co= A   i ×1.19=87398 Bq 
   Hence, the calibrated gross gamma radioactivity A t =250517 Bq
         the standard gross gamma radioactivity is 246239 Bq   the deviation of correctness is 1.74%       

   
     
       
             
           
             
             
             
             
             
             
           
         
             
               TABLE 3 
             
           
           
             
                 
             
             
               nuclide parameters for calibration phantoms of various 
             
             
               densities 
             
           
        
         
             
               parameter 
               gcm −3   
                 57 Co 
                 54 Mn 
                 60 Co 
                 137 Cs 
             
             
                 
             
             
               R x   
                 
               0.593 
               0.628 
               1.19 
               1 
             
             
               p x   
                 
                96% 
                100% 
                200% 
                 85% 
             
             
               ε x   
               1.1 
               3.5% 
               14.5% 
               16.6% 
               17.7% 
             
             
               ε x   
               1.8 
               2.5% 
               11.4% 
               14.1% 
               14.5% 
             
             
               ε x   
               2.5 
               2.4% 
               11.1% 
               12.7% 
               13.2% 
             
             
                 
             
           
        
       
     
   
   To sum up, the volume calibration phantom and calibration method thereof disclosed in the present invention have the following advantages:
         (1) The MDAs of  57 Co,  54 Mn,  60 Co are 5 times lower than the release standard specified by authority, that the volume calibration phantom is suitable for measuring a box of uniform nuclear waste.   (2) As the waste is a multi-nuclide waste, the gross gamma radioactivity is calibrated with respect to parameters, such as A i , ε i , p i , R x , E x , so that it is deviated from the standard radioactivity no more than 5%.   (3) The radioactivity uniformity of a multi-density volume calibration phantom composed of four uniform radionuclides is smaller than 7.9%.   (4) The range of the density and energy level of an so-established volume calibration phantom is comparatively wide, so that the accuracy of measurement is enhanced.       

   While the preferred embodiment of the invention has been set forth for the purpose of disclosure, modifications of the disclosed embodiment of the invention as well as other embodiments thereof may occur to those skilled in the art. Accordingly, the appended claims are intended to cover all embodiments which do not depart from the spirit and scope of the invention.